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Economics, section 1, Fall 2019
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Camm, et al - Intro to Management Science - 16/e (Homework)

James Finch

Economics, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 35 / 122

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving... ()

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Question

Points

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
0/2	–/4	–/9	10/12	9/16	0/10	–/8	12/17	1/1	1/1	1/1	0/3	1/1	–/10	0/1	–/1	–/23	0/1	–/1

Total

35/122 (28.7%)

Instructions

WebAssign provides a wide range of exercises that enable you to:

Build problem-solving skills (#1-3: Read It, Watch It, and Master It, exercises)
Develop conceptual understanding (#4-7: Stand-alone Master It, Personalized Feedback, and Alternative Optima exercises)
Address readiness gaps and assess summative understanding (#8-9: Excel tutorial and Test Bank exercises)

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1. 0/2 points | Previous Answers CammIMS16 2.E.010. My Notes

This exercise will build problem-solving skills.
Read It links are available as a learning tool under each question so students can quickly jump to the corresponding section of the eTextbook.

For the linear program

Max

2A + 3B

s.t.

1A	+	2B ≤ 4
5A	+	3B ≤ 15
	A,	B ≥ 0

find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution?

d

$webMathematica generated answer key$ at (A, B) =

$webMathematica generated answer key$

Solution or Explanation

The A B-coordinate plane is given. There are 2 lines and a shaded region on the graph.
The first line labeled A + 2B = 4 enters the window at B = 2 on the positive B-axis, goes down and right, passes through the approximate point (2.57, 0.71) crossing the second line labeled 5A + 3B = 15, and exits the window at A = 4 on the positive A-axis.
The second line labeled 5A + 3B = 15 enters the window at B = 5 on the positive B-axis, goes down and right, passes through the approximate point (2.57, 0.71) crossing the first line labeled A + 2B = 4, and exits the window at A = 3 on the positive A-axis.
The region is below the first line labeled A + 2B = 4 and below the second line labeled 5A + 3B = 15.
The intersection of the lines is labeled Optimal Solution.
The value of the objective function is labeled 2(18⁄7) + 3(5⁄7) = 51⁄7.

(1)

(2)

(1) ✕ 5

10B

(3)

(2) − (3)

−

−5

From (1),

A = 4 − 2

= 4 −

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2. –/4 points CammIMS16 15.E.001. My Notes

This exercise will build problem-solving skills.
Students get just-in-time learning support with Watch It videos that contain narrated and closed-captioned videos walking students through the proper steps to solve a similar problem.

Consider the following time series data.

Week	1	2	3	4	5	6
Value	19	13	16	12	16	13

Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy.

(a)

mean absolute error

MAE =

(b)

mean squared error

MSE =

(c)

mean absolute percentage error (Round your answer to two decimal places.)

MAPE = %

(d)

What is the forecast for week 7?

Need Help?

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3. –/9 points CammIMS16 13.E.001.MI. My Notes

This exercise will build problem-solving skills.
Master It tutorials are an optional student-help tool available within select questions for just-in-time support. Students can use the tutorial to guide them through the problem-solving process step-by-step using different numbers.

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.

Decision Alternative	States of Nature
Decision Alternative	s₁	s₂	s₃
d₁	260	110	35
d₂	110	110	85

(a)

Construct a decision tree for this problem.

Decision Tree

Description

A decision tree begins at decision node 1 and an upper and lower branch extend from this node to the right. The upper branch, labeled d₁, stops at chance node 2 and an upper, middle and lower branch extend from this node to the right. The lower branch, labeled d₂, stops at chance node 3 and an upper, middle and lower branch extend from this node to the right.
The branches extending from decision node 1 from top to bottom are labeled d₁ and d₂. The next set of branches from top to bottom are labeled s₁, s₂, s₃, s₁, s₂ and s₃. There is an answer blank at the end of each branch.

(b)

If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

The recommended decision using the optimistic approach is . The recommended decision using the conservative approach is . The recommended decision using the minimax regret approach is .

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4. 10/12 points | Previous Answers CammIMS16 13.E.001.MI.SA. My Notes

This exercise will build problem-solving skills.
Master It tutorials—Standalone are embedded, step-by-step tutorials used to help students understand each step required to solve the problem, before inputting their final answer.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.

Decision Alternative	States of Nature
Decision Alternative	s₁	s₂	s₃
d₁	230	80	5
d₂	80	80	55

(a)

Construct a decision tree for this problem.

(b)

If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

Step 1

(a) Construct a decision tree for this problem.

A decision tree is a graphical representation that shows the sequential nature of the decision-making process. Watch the video to learn how to create a decision tree for this scenario.

Recall the given data.

Decision Alternative	States of Nature
Decision Alternative	s₁	s₂	s₃
d₁	230	80	5
d₂	80	80	55

The decision tree for this problem is as follows.

Decision Tree

Correct: Your answer is correct. — A decision tree has 6 answer blanks. Refer to the adjacent list for more details.

Description

A decision tree begins at decision node 1 and an upper and lower branch extend from this node to the right. The upper branch, labeled d₁, stops at chance node 2 and an upper, middle and lower branch extend from this node to the right. The lower branch, labeled d₂, stops at chance node 3 and an upper, middle and lower branch extend from this node to the right.
The branches extending from decision node 1 from top to bottom are labeled d₁ and d₂. The next set of branches from top to bottom are labeled s₁, s₂, s₃, s₁, s₂ and s₃. There is an answer blank at the end of each branch.

(b) If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

When probabilities for decision alternatives are not available, the optimistic, conservative, and minimax regret approaches can be used. The optimistic approach leads to choosing the decision alternative that leads to the smallest or largest payoff, for minimization and maximization problems, respectively. The conservative approach leads to choosing the decision alternative that maximizes the minimum payoff; for a minimization problem, it leads to choosing the decision alternative that minimizes the maximum payoff. The minimax regret approach involves calculating the maximum regret for each alternative and choosing the decision alternative that minimizes the maximum regret.

Watch the video to determine which decisions should be selected for each approach.

Recall the decision tree.

A decision tree begins at decision node 1 and an upper and lower branch extend from this node to the right. The upper branch, labeled d₁, stops at chance node 2 and an upper, middle and lower branch extend from this node to the right. The lower branch, labeled d₂, stops at chance node 3 and an upper, middle and lower branch extend from this node to the right.

The branches extending from decision node 1 from top to bottom are labeled d₁ and d₂. The next set of branches from top to bottom are labeled s₁, s₂, s₃, s₁, s₂ and s₃. The values to the right of these branches are 230, 80, 5, 80, 80, and 55 respectively.

Using the optimistic approach, the largest maximum profit is

230

by decision

d₁

Using the conservative approach, the largest minimum profit is

by decision

d₂

Using the minimax regret approach, decision

d₁

minimizes the maximum regret with a value of

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5. 9/16 points | Previous Answers CammIMS16 3.E.009. My Notes

6. 0/10 points | Previous Answers CammIMS16 4.E.009. My Notes

This exercise will develop conceptual understanding.

Personalized numerical feedback addresses common student mistakes including improper rounding, inadvertently including or not including a sign, incorrect fraction formatting and more. To view some of the feedback, try doing one of the following:
- For the 1st algebraic answer blank (labeled Min), enter lower case variables instead of upper case variables.
- For the 1st algebraic answer blank (labeled Min), type in a letter not included in the set like W, Z, or a.
- For the 2nd through 8th algebraic answer blanks (labeled Monday–Friday), enter an equals sign instead of an inequality.
- For the 2nd through 8th algebraic answer blanks (labeled Monday–Friday), enter the wrong letter for one of the variables.
- For the 9th and 10th algebraic answer blanks (labeled (X₁, X₂, X₃, X₄, X₅, X₆, X₇) =, and (M, Tu, W, Th, F, Sa, Su) =), shuffle the order of a couple of the distinct numbers.
- For the 9th and 10th algebraic answer blanks (labeled (X₁, X₂, X₃, X₄, X₅, X₆, X₇) =, and (M, Tu, W, Th, F, Sa, Su) =), remove one of the numbers.

A linear programming computer package is needed.

Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of Epsilon's customers make reservations through Epsilon's website, but a small percentage of customers make reservations via phone. Epsilon employs call-center personnel to handle these reservations along with any problems with the website reservation system and for the rebooking of flights for customers if their plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon's management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers.

Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are given in the following table.

Day	Minimum Number of Employees Needed
Monday	80
Tuesday	50
Wednesday	45
Thursday	65
Friday	100
Saturday	90
Sunday	50

The call-center employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each call-center employee receives the same salary. Assume that the schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the total number of call-center employees needed to meet the minimum requirements. (Let

X_i

= the number of call-center employees who start work on day i where

i = 1 = Monday,

i = 2 = Tuesday,

etc).

Min

a

s.t. Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

X₁, X₂, X₃, X₄, X₅, X₆, X₇ ≥ 0

Find the optimal solution.

(X₁, X₂, X₃, X₄, X₅, X₆, X₇) =

Give the number of call-center employees that exceed the minimum required.

(M, Tu, W, Th, F, Sa, Su) =

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7. –/8 points CammIMS16 7.E.013. My Notes

This exercise will develop conceptual understanding.

Alternative optima solutions are supported. Students can enter any ordered list that satisfies the indicated constraints and will be marked correct.

The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas. The following is a linear program used to determine which cities Martin-Beck should construct a plant in.

Let

y₁ = 1 if a plant is constructed in Detroit; 0 if not

y₂ = 1 if a plant is constructed in Toledo; 0 if not

y₃ = 1 if a plant is constructed in Denver; 0 if not

y₄ = 1 if a plant is constructed in Kansas City; 0 if not.

The variables representing the amount shipped from each plant site to each distribution center are defined just as for a transportation problem.

x_ij = the units shipped in thousands from plant i to distribution center j

i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St.Louis) and

j = 1 (Boston), 2 (Atlanta), 3 (Houston)

The complete model for the Martin-Beck distribution system design problem is as follows.

Min 5x₁₁ + 2x₁₂ + 3x₁₃ + 4x₂₁ + 3x₂₂ + 4x₂₃ + 9x₃₁ + 7x₃₂ + 5x₃₃ + 10x₄₁ + 4x₄₂

+ 2x₄₃ + 8x₅₁ + 4x₅₂ + 3x₅₃ + 175y₁ + 300y₂ + 375y₃ + 500y₄

s.t.

x₁₁	+	x₁₂	+	x₁₃					≤ 10y₁	Detroit capacity

x₂₁	+	x₂₂	+	x₂₃					≤ 20y₂	Toledo capacity

x₃₁	+	x₃₂	+	x₃₃					≤ 30y₃	Denver capacity

x₄₁	+	x₄₂	+	x₄₃					≤ 40y₄	Kansas City capacity

x₅₁	+	x₅₂	+	x₅₃					≤ 30	St. Louis capacity

x₁₁	+	x₂₁	+	x₃₁	+	x₄₁	+	x₅₁	= 30	Boston demand

x₁₂	+	x₂₂	+	x₃₂	+	x₄₂	+	x₅₂	= 20	Atlanta demand

x₁₃	+	x₂₃	+	x₃₃	+	x₄₃	+	x₅₃	= 20	Houston demand

x_ij ≥ 0 for all i and j; y₁, y₂, y₃, y₄ = 0, 1

(a)

Modify the original formulation to account for the policy restriction that there must be one plant in either Detroit or Toledo, but not both.

new constraint

(y₁, y₂, y₃, y₄)

Place

x_ij

in row i column j.

value =

(b)

Modify the original formulation to account for the policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis.

new constraint

(y₁, y₂, y₃, y₄)

Place

x_ij

in row i column j.

value =

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8. 12/17 points | Previous Answers CammIMS16 A.ET.004. My Notes

This exercise will address readiness gaps.

This question covers basic Excel functionality that will be useful throughout the textbook.

Microsoft Excel File

Introduction

Frequently, you will have data that, instead of being numerical, is text based. The data could be names of people, businesses, or longer form text you would like to mine for information. While Excel is primarily designed to deal with and manipulate numbers, it also has a set of tools that help you work with text information efficiently and easily. This tutorial is designed to familiarize you with those tools in a common and easy to understand situation.

The data has been collected in the Microsoft Excel file. Open the spreadsheet and perform the required analysis to answer the questions below.
Common Text Functions

Functions such as PROPER, LEN, LEFT, and RIGHT allow you to clean up and parse text information that may arrive to you in a less than ideal format. Practice using these functions in cells D2:D5 using the data in column C. (Enter your answers exactly as they appear in the excel spreadsheet.)

Name data to proper case Number of characters in a text string Find first 4 characters of a text string Find final 3 characters of a text string

While LEFT and RIGHT are straightforward, the MID function will provide the middle portion of a text string. You just need to tell it where to begin and how many characters you want after that location.

In cell D6, get three characters from the text string in C6 starting on the third character. (Enter the characters exactly as they appear.)
Concatenation

Concatenation is a very common task in Excel (and in many other programming languages). To concatenate means to bring or "stick" things together. A common example is to have first name and last name and a need to bring those together for a full name. In Excel there are several ways to concatenate text strings.

The easiest is the CONCAT function. All you do is tell it which cells you want stuck together. Try doing that in cell D7. (Enter the result for D7 exactly as it appears in the spreadsheet in the blank below.)

Concatenate (bring together) text strings:
JenniferClarke

However, CONCAT is very literal. It doesn't know that there should be a space between a first and last name for example. Therefore, you need to add that space to the CONCAT function. In Excel, a blank space is represented by the " " string of characters; quote-space-quote. Add that to the CONCAT function and practice in cell D8. (Enter the result for D8 exactly as it appears in the spreadsheet in the blank below.)

Concatenate (bring together) text strings adding a space, " ":
Jennifer Clarke

You can also concatenate by using ampersand (&) calculation operator instead of the CONCAT function. Again, include a space represented by the " " into your formula. Practice that in cell D9. (Enter the result for D9 exactly as it appears in the spreadsheet in the blank below.)

Concatenate (bring together) text strings using ampersand (&) and adding a space, " ":
Jennifer Clarke
Number Conversion

Not all numbers should be treated as "numbers" in a dataset. For example, zip codes, phone numbers, addresses, etc., are not meant to be added, subtracted, divided, or multiplied. Adding zip codes makes no sense. Therefore, those types of data should actually be treated as text. Luckily, Excel has the TEXT function which will do that easily. The TEXT function also requires that you tell Excel how to format the result. In the case of a zip code, we want five characters: "#####" (use the quotation marks). Use the TEXT function and the "#####" formatting rule to convert the number in C10 to a text zip code in cell D10. (Enter the result for D10 exactly as it appears in the spreadsheet in the blank below.)

Convert a number (like a zip code) to text:
48728

One challenge with converting zip codes and other numbers is that some of those values start with a leading zero. For numbers, a leading zero does not mean anything. However, for a zip code, it means a lot! Therefore, when converting a zip code that is supposed to have a leading zero, a slightly different formatting is required: "0####" which instructs Excel to format the text as 0 then the four numbers. Use that formatting technique in cell D11. (Enter the results for D11 exactly as it appears in the spreadsheet in the blank below.)

Convert a number (like a zip code) to text adding back leading zero:
06486
Searching and Splitting

Sometimes you need to search for the location of the first occurrence of a character or sub-string within a larger string. A common example is to find the location of the "@" symbol in an email address so you can isolate the username of the address. In cell D12, find the location of the "@" symbol in the email address in cell C12.

Search for the location of the text string "@" within an email address:
8

Finally, you can combine SEARCH and LEFT to isolate the username of the email address. SEARCH tells you where the "@" symbol is located and LEFT needs to know how many characters on the left you want to keep; which SEARCH can provide. Try combining SEARCH and LEFT in cell D13 to isolate the email username from cell C13. (Enter the result for D13 exactly as it appears in the spreadsheet in the blank below.)

Note: there is one slight modification you will need to make to the SEARCH part of the formula to get just the username. See if you can figure it out.

Split off username from email address. Hint: search for @ symbol:
jclarke

Text Data Cleaning and Manipulation

Beginning in row 16, columns B and C contain raw names and numeric zip codes. In columns D through H, you are asked to clean and manipulate that data in specific ways. The good thing is that you only have to create formulas for the first row and then you can fill down. Enter the values for the last row below.

Note: These are meant to be challenging. So just take your time and work though each column logically using trial and error if necessary.

Hint: The last column for zip code, will require a nested IF function to first see if the numeric zip code is 5 or 4 characters long so you then know which formatting to apply. (Enter your answers exactly as they appear in the excel spreadsheet. Remember the first letter of the First name and the first letter of the Last name should be capitalized.)

Proper Name	First Name	Last Name	Short Name (First L.)	New Zip Code
Bowen Summers	Bowen	Summers	Bowen S.	06316

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9. 1/1 points | Previous Answers CammIMS16 5.TB.022. My Notes

This exercise will assess summative understanding.

This question is representative of the test bank questions offered in this title either via Cognero or directly in WebAssign.

A DEA linear programming model involving five input measures and four output measures will have how many constraints?

10 20 21

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10. 1/1 points | Previous Answers CammIMS16 1.TB.026. My Notes

In a multicriteria decision problem

successive decisions must be made over time. it is impossible to select a single decision alternative. correct

the decision maker must evaluate each alternative with respect to each criterion. all of these statements apply.

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11. 1/1 points | Previous Answers CammIMS16 2.TB.016. My Notes

The boundary of the constraint 3x₁ − 6x₂≤ 0 passes through the point

(x₁, x₂) = (60, 30).

True False

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12. 0/3 points | Previous Answers CammIMS16 2.TB.045. My Notes

Consider the following linear programming problem:

Max	9X + 6Y
s.t.
	14X + 5Y	≤	70
	12X + 6Y	≤	72
	X + Y	≤	11
	X, Y ≥ 0

(a)

Use a graph to show each constraint and the feasible region.

The X Y-coordinate plane is given. There are 3 lines and a shaded region on the graph.
The first line enters the window at Y = 5 on the positive Y-axis, goes down and right, passes through the point (7, 2.5) crossing the second line, passes through the approximate point (9.3, 1.7) crossing the third line, and exits the window at X = 14 on the positive X-axis.
The second line enters the window at Y = 6 on the positive Y-axis, goes down and right, passes through the point (7, 2.5) crossing the first line, passes through the point (10, 1) crossing the third line, and exits the window at X = 12 on the positive X-axis.
The third line enters the window at Y = 11 on the positive Y-axis, goes down and right, passes through the approximate point (9.3, 1.7) crossing the first line, passes through the point (10, 1) crossing the second line, and exits the window at X = 11 on the positive X-axis.
The region is below the first line, below the second line, below the third line, above the horizontal axis, and right of the vertical axis.

The X Y-coordinate plane is given. There are 3 lines and a shaded region on the graph.
The first line enters the window at Y = 14 on the positive Y-axis, goes down and right, passes through the approximate point (1.7, 9.3) crossing the third line, passes through the point (2.5, 7) crossing the second line, and exits the window at X = 5 on the positive X-axis.
The second line enters the window at Y = 12 on the positive Y-axis, goes down and right, passes through the point (1, 10) crossing the third line, passes through the point (2.5, 7) crossing the first line, and exits the window at X = 6 on the positive X-axis.
The third line enters the window at Y = 11 on the positive Y-axis, goes down and right, passes through the point (1, 10) crossing the second line, passes through the approximate point (1.7, 9.3) crossing the first line, and exits the window at X = 11 on the positive X-axis.
The region is below the first line, below the second line, below the third line, above the horizontal axis, and right of the vertical axis.

(b)

Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?

(X, Y) =

(c)

What is the optimal value of the objective function?

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13. 1/1 points | Previous Answers CammIMS16 3.TB.043. My Notes

In a linear programming problem, the binding constraints for the optimal solution are:

7X + 5Y ≤ 50
2X + 7Y ≤ 20

The current optimal solution point will remain optimal as long as the slope of the objective function stays between

−

and

−

2 7

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14. –/10 points CammIMS16 3.TB.049. My Notes

Consider the following spreadsheet and Excel Solver sensitivity report. (The profit is in dollars, and the variables x₁ and x₂ represent the number of units of products 1 and 2, respectively.)

	A	B	C	D	E
1
2	Input Information
3		x₁	x₂	(type)	Avail.
4	Constraint 1	2	5	<	42
5	Constraint 2	3	1	<	34
6	Constraint 3	1	1	>	11
7
8	Profit	6	3
9
10	Output Information
11	Variables
12	Profit				= Total
13
14	Resources	Used	Slack/Surplus
15	Constraint 1
16	Constraint 2
17	Constraint 3
18
19

Sensitivity Report

Variable Cells
Cell	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
$B$11	Variables x₁	9.846153846	0	6	3	4.8
$C$11	Variables x₂	4.461538462	0	3	12	1

Constraints
Cell	Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
$B$15	Constraint 1 Used	42	0.2307692308	42	128	19.333333333
$B$16	Constraint 2 Used	34	1.846153846	34	29	14.333333333
$B$17	Constraint 3 Used	14.30769231	0	11	3.307692308	1E+30

Use the spreadsheet and Excel Solver sensitivity report to answer these questions.

(a)

What is the cell formula for B12 (the profit contribution of variable x₁)?

(b)

What is the cell formula for C12 (the profit contribution of variable x₂)?

(c)

What is the cell formula for D12?

(d)

What is the cell formula for B15 (the final value of the first constraint)?

(e)

What is the cell formula for B16 (the final value of the first constraint)?

(f)

What is the cell formula for B17 (the final value of the first constraint)?

(g)

What is the optimal value for x₁? (Round your answer to two decimal places.)

(h)

What is the optimal value for x₂? (Round your answer to two decimal places.)

(i)

Would you pay $0.20 each for up to 76 more units of resource 1?

Yes No

(j)

Is it possible to figure the new objective function value if the profit on product 1 increases by a dollar, or do you have to rerun Solver?

Yes, it is possible to know the new value without rerunning Solver. No, it is necessary to rerun Solver.

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15. 0/1 points | Previous Answers CammIMS16 4.TB.021. My Notes

To study consumer characteristics, attitudes, and preferences, a company would engage in

capital budgeting. client satisfaction processing. production planning. marketing research.

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16. –/1 points CammIMS16 4.TB.039. My Notes

An ice cream company must decide how much money to allocate for advertising both their new flavor of ice cream and a traditional flavor over the coming year. The advertising budget is $18,000,000. Because the company wants to push its new flavor, at least one-half of the advertising budget is to be devoted to the new flavor advertising. However, at least $3,600,000 is to be spent on its traditional flavor. The company estimates that each dollar spent on the traditional flavor will translate into 50 pints sold, whereas, because of the harder sell needed for new products, each dollar spent on the new flavor will translate into 100 pints sold.

To attract new customers, the company has lowered its profit margin on the new flavor to 2 cents per pint as compared to 4 cents per pint for the traditional flavor. The company wants to sell at least 750 million pints total. What is their maximum profit?

$50 million $45 million $43 million $40 million

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17. –/23 points CammIMS16 5.TB.045. My Notes

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Submissions Used

–/1

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An airline provides passenger service for Indianapolis, Baltimore, Memphis, Austin, and Tampa. The airline has two WB828 airplanes, one based in Indianapolis and the other in Baltimore. Each morning, the Indianapolis-based plane flies to Austin with a stopover in Memphis, and the Baltimore-based plane flies to Tampa with a stopover in Memphis. Both planes have a coach section with a 120-seat capacity.

The airline uses two fare classes: a discount-fare D class and a full-fare F class. The airline's products, each referred to as an origin-destination-itinerary fare (ODIF), are listed below with their fares (in dollars) and forecasted demand.

ODIF	Origin	Destination	Fare Class	ODIF Code	Fare	Demand
1	Indianapolis	Memphis	D	IMD	175	43
2	Indianapolis	Austin	D	IAD	275	24
3	Indianapolis	Tampa	D	ITD	285	39
4	Indianapolis	Memphis	F	IMF	395	16
5	Indianapolis	Austin	F	IAF	425	9
6	Indianapolis	Tampa	F	ITF	475	7
7	Baltimore	Memphis	D	BMD	185	25
8	Baltimore	Austin	D	BAD	315	49
9	Baltimore	Tampa	D	BTD	290	41
10	Baltimore	Memphis	F	BMF	385	11
11	Baltimore	Austin	F	BAF	525	17
12	Baltimore	Tampa	F	BTF	490	8
13	Memphis	Austin	D	MAD	190	57
14	Memphis	Tampa	D	MTD	180	47
15	Memphis	Austin	F	MAF	310	13
16	Memphis	Tampa	F	MTF	295	10

Develop a linear programming model for the airline's problem situation which maximizes total revenue (in dollars). (Let the variables be IMD, IAD, ITD, …, MTF where each variable represents the number of seats allocated to the corresponding ODIF. Enter your demand constraints as comma-separated lists of inequalities.)

Max

s.t. Indianapolis-Memphis leg capacity

Baltimore-Memphis leg capacity

Memphis-Austin leg capacity

Memphis-Tampa leg capacity

D class demand

F class demand

all variables ≥ 0

Determine how many seats the airline should allocate to each ODIF.

ODIF	Number of Seats
IMD
IAD
ITD
IMF
IAF
ITF
BMD
BAD
BTD
BMF
BAF
BTF
MAD
MTD
MAF
MTF

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18. 0/1 points | Previous Answers CammIMS16 6.TB.023. My Notes

There are two specific types of problems common in supply chain models that can be solved using linear programming: transportation problems and transshipment problems.

True False

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19. –/1 points CammIMS16 7.TB.037. My Notes

Assuming W₁, W₂, and W₃ are 0-1 integer variables, the constraint W₁ + W₂ + W₃ ≤ 1 is often called a

multiple-choice constraint. k out of n alternatives constraint. corequisite constraint. mutually exclusive constraint.

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Max	1W	+	1.25M
s.t.
	5W	+	7M	≤	4,560	oz of whole tomatoes
	3W	+	1M	≤	2,240	oz of tomato sauce
	2W	+	2M	≤	1,600	oz of tomato paste
	W,	M	≥ 0

Variable	Value	Reduced Cost
W	520.00000	0.00000
M	280.00000	0.00000

Constraint	Slack/Surplus	Dual Value
1	0.00000	0.12500
2	400.00000	0.00000
3	0.00000	0.18750

Variable	Objective Coefficient	Allowable Increase	Allowable Decrease
W	1.00000	0.25000	0.10714
M	1.25000	0.15000	0.25000

Constraint	RHS Value	Allowable Increase	Allowable Decrease
1	4560.00000	1040.00000	400.00000
2	2240.00000	Infinite	400.00000
3	1600.00000	100.00000	297.14286

1	2	3	4	5	6	7	8	9	10	11	12
1/1	1/1	1/1	1/1	1/1	1/1	1/1	1/1	1/1	1/1	0/1	0/1
1/100	1/100	1/100	1/100	1/100	1/100	1/100	1/100	1/100	1/100	1/100	1/100

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Camm, et al - Intro to Management Science - 16/e (Homework)

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(a) Construct a decision tree for this problem.

(b) If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

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