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MNS407 Management Science, Fall 2024

407 Module 2: Quiz#2 (Quiz) INSTRUCTOR

Vahid Keyhani National University, La Jolla CA

Current Score

QUESTION

POINTS

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TOTAL SCORE

–/10 0.0%

SUN, NOV 10, 2024

11:59 PM PST

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This Quiz covers material in Chapters 4 and 6. You have one attempt to submit your answers.

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11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=35936172 1/15

A local television station plans to drop four Friday evening programs at the end of the season. Steve Botuchis, the station manager, developed a list of six potential replacement programs. Estimates of the advertising revenue ($) that can be expected for each of the new programs in the four vacated time slots are as follows.

5:00–5:30 p.m. 5:30–6:00 p.m. 7:00–7:30 p.m. 8:00–8:30 p.m.

Comedy Live 5,000 3,000 6,000 4,000

World News 7,500 8,000 7,000 5,500

NASCAR Live 8,500 5,000 6,500 8,000

Wall Street Today 7,000 6,000 6,500 5,000

Hollywood Briefings 7,000 8,000 3,000 6,000

This Week in Hockey 6,000 4,000 4,500 7,000

Mr. Botuchis asked you to find the assignment of programs to time slots that will maximize total advertising revenue.

Optimal Solution

5:00–5:30 p.m. ---Select---

5:30–6:00 p.m. ---Select---

7:00–7:30 p.m. ---Select---

8:00–8:30 p.m. ---Select---

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(Optional)

1. [–/0.76 Points] ASWMSCI15 6.E.019.DETAILS MY NOTES

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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A grocery store manager must decide how to best present a limited supply of popcorn and soda to its customers. Popcorn can be sold by itself for a profit of $1.40 per tin. Soda can likewise be sold at a profit of $2.40 per liter. To increase appeal to customers, one tin of popcorn and a liter of soda can be packaged together and sold for a profit of $3.30 per bundle. The manager has at most 120 tins of popcorn and 170 liters of soda to make available each day. The manager has decided to stock at least 65 individual tins of popcorn per day (excluding popcorn bundled with soda). Demand for individual liters of soda is at most 160 liters per day (excluding soda bundled with popcorn). The manager wishes to determine how much of each product to stock each day.

Which of the following is the objective function for the grocer's problem? (Let P be the number of individual tins of popcorn stocked each day. Let S be the number of individual sodas stocked each. Let B be the number of bundles stocked. Assume that, within the limitations established by the constraints, the store can sell all the products it stocks.)

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(Optional)

The assignment problem constraint x + x + x + x ≤ 1 means

there is no feasible solution.

agent 1 can be assigned to three tasks.

a mixture of agents 1, 2, 3, and 4 will be assigned to tasks.

agent 3 can be assigned to one task.

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(Optional)

Min 2.4P + 3.3S + 1.4B

Min 1.4P + 2.4S + 3.3B

Max 2.4P + 1.4S + 3.3B

Max 1.4P + 2.4S + 3.3B

31 32 33 34

2. [–/0.76 Points] CAMMIMS16 4.TB.035.DETAILS MY NOTES PRACTICE ANOTHER

3. [–/0.76 Points] CAMMIMS16 6.TB.033.DETAILS MY NOTES

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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Which of the following is true regarding an LP model of the assignment problem?

The objective function value is either 0 or 1.

The number of constraints is calculated as number of origins times number of destinations.

All decision variable values are either 0 or 1.

All constraints are of the ≥ form.

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(Optional)

An LP model for a marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories. There is a constraint that The solution indicates that interviewing another homeowner during the day will increase costs by $5.00. What does this tell you about the HD variable?

The dual price for the HD constraint is 5.

The objective function coefficient of HD is −5.

The objective function coefficient of HD is 5.

The dual price for the HD constraint is −5.

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(Optional)

HD ≥ 120.

4. [–/0.76 Points] CAMMIMS16 6.TB.032.DETAILS MY NOTES

5. [–/0.76 Points] ASWMSCI15 4.TB.023.DETAILS MY NOTES PRACTICE ANOTHER

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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Draw the network for this transportation problem. (Let x represent the flow from node i to node j.)ij

Min 2x + 4x + 6x + 10x + 11x + 11x13 14 15 23 24 25 s.t.

x + x + x ≤ 500 x + x + x ≤ 400

x + x = 300 x + x = 300 x + x = 300

x ≥ 0

13 14 15

23 24 25

13 23

14 24

15 25

ij

6. [–/0.76 Points] CAMMIMS16 6.TB.050.DETAILS MY NOTES PRACTICE ANOTHER

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Show My Work

(Optional)

ℹ ℹ ℹ

ℹ

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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Consider the following shortest-route problem involving six cities with the distances given.

Path Distance

1 to 2 4

1 to 3 2

2 to 4 5

2 to 5 4

3 to 4 4

3 to 5 8

4 to 6 7

5 to 6 2

Draw the network for this problem.

7. [–/0.88 Points] CAMMIMS16 6.TB.060.DETAILS MY NOTES PRACTICE ANOTHER

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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Formulate the LP for finding the shortest distance from City 1 to City 6. (Let x represent the flow from node i to node j.)

Min

s.t. Node 1 Flows

Node 2 Flows

ℹ ℹ

ℹ ℹ

ij

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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Node 3 Flows

Node 4 Flows

Node 5 Flows

Node 6 Flows

x > 0 for all i and j

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(Optional)

ij

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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City Cab Company identified 10 primary pickup and drop locations for cab riders in New York City. In an effort to minimize travel time and improve customer service and the utilization of the company's fleet of cabs, management would like the cab drivers to take the quickest route between locations whenever possible. The travel times in minutes are shown on the arcs of the network. Note that there are two one- way streets and that the direction is shown by the arrows.

Using the above network of roads and streets, what is the quickest route a driver beginning at location 1 should take to reach location 10?

path = 1,

, 10

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(Optional)

ℹ

8. [–/0.76 Points] ASWMSCI15 6.E.027.DETAILS MY NOTES

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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The north-south highway system passing through Albany, New York, can accommodate the capacities shown.

Can the highway system accommodate a north-south flow of 10,000 vehicles per hour?

Yes

No

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(Optional)

ℹ

9. [–/0.76 Points] ASWMSCI15 6.E.029.DETAILS MY NOTES

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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After some special presentations, the employees of an event planning center have to move dining chairs back to their original storage locations. The table below indicates the buildings where the chairs are now (the sources), where they need to go (the destinations), and a measure of the distance between sites.

Source Destination

Supply Business Education Parsons Hall Holmstedt Hall

Baker Hall 9 8 4 2 34

Tirey Hall 13 10 1 7 9

Arena 14 13 6 5 19

Demand 13 19 9 11

(a) If you were going to write this as a linear programming model, how many decision variables would there be?

How many constraints would there be?

The solution to this problem is shown below. Use it to answer parts (b) through (e).

Transportation Problem

Optimal Transportation Schedule

From To Destination

From Origin 1 2 3 4

1 13 19 0 2

2 0 0 9 0

3 0 0 0 9

Total Transportation Cost or Revenue is 327 Note: The Total Supply Exceeds The Todal Demand By 10

Origin Excess Supply

3 10

(b) How many chairs are moved from Baker to Business?

10. [–/0.76 Points] CAMMIMS16 6.TB.052.DETAILS MY NOTES PRACTICE ANOTHER

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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(c) How many chairs are moved from Tirey to Parsons?

(d) How many chairs are moved from Arena to Education?

(e) Which site(s) has (have) chairs left? (Select all that apply.)

Baker Hall

Tirey Hall

Arena

Business

Education

Parsons Hall

Holmstedt Hall

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(Optional)

Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then

−0.5A + 0.5B − 0.5C ≤ 0.

B ≤ 5.

A − 0.5B + C ≤ 0.

0.5A − B − 0.5C ≤ 0.

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(Optional)

11. [–/0.76 Points] CAMMIMS16 4.TB.027.DETAILS MY NOTES

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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A linear programming computer package is needed.

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows.

Component Supplier

1 2 3

1 $11 $12 $13

2 $9 $10 $9

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows.

Supplier 1 2 3

Capacity 800 1,200 1,000

If the Edwards production plan for the next period includes 1,200 units of component 1 and 1,000 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier?

Component 1, Supplier 1 units

Component 1, Supplier 2 units

Component 1, Supplier 3 units

Component 2, Supplier 1 units

Component 2, Supplier 2 units

Component 2, Supplier 3 units

What is the total purchase cost (in $) for the components?

$

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(Optional)

12. [–/0.76 Points] ASWMSCI15 4.E.011.DETAILS MY NOTES PRACTICE ANOTHER

11/3/24, 10:48 PM 407 Module 2: Quiz#2 - MNS407 Management Science, Fall 2024 | WebAssign

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In a production scheduling LP, the demand requirement constraint for a time period takes the form

Beginning inventory − Production + Ending inventory = Demand.

Beginning inventory + Production + Ending inventory ≥ Demand.

Beginning inventory + Production − Ending inventory = Demand.

Beginning inventory − Production − Ending inventory ≥ Demand.

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13. [–/0.76 Points] CAMMIMS16 4.TB.030.DETAILS MY NOTES

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