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7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | WebAssign
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MNS407 Management Science, Summer 1 2023
407 Module 2: Quiz#2 (Quiz) INSTRUCTOR
Karen Joiner
National University, La Jolla CA
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QUESTION
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SUN, JUL 16, 2023
11:59 PM MST
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7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=31948009#question4538525_9 2/17
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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1. [–/0.76 Points] ASWMSCI15 4.E.011.DETAILS
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7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | WebAssign
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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.
0.5A − B − 0.5C ≤ 0.
A − 0.5B + C ≤ 0.
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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 $15.00. What does this tell you about the HD variable?
The dual price for the HD constraint is −15.
The objective function coefficient of HD is 15.
The objective function coefficient of HD is −15.
The dual price for the HD constraint is 15.
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HD ≥ 120.
2. [–/0.76 Points] CAMMIMS16 4.TB.027.DETAILS MY NOTES ASK YOUR TEACHER
3. [–/0.76 Points] ASWMSCI15 4.TB.023.DETAILS
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7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | 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 $3.30 per bundle. The manager has at most 120 tins of popcorn and 140 liters of soda to make available each day. The manager has decided to stock at least 85 individual tins of popcorn per day (excluding popcorn bundled with soda). Demand for individual liters of soda is at most 130 liters per day (excluding soda bundled with popcorn). The manager wishes to determine how much of each product to stock each day.
Which of the following is the objective function for the grocer's problem? (Let P be the number of individual tins of popcorn stocked each day. Let S be the number of individual sodas stocked each. Let B be the number of bundles stocked. Assume that, within the limitations established by the constraints, the store can sell all the products it stocks.)
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Min 1.4P + 2.4S + 3.3B
Min 2.4P + 3.3S + 1.4B
Max 2.4P + 1.4S + 3.3B
Max 1.4P + 2.4S + 3.3B
4. [–/0.76 Points] CAMMIMS16 4.TB.035.DETAILS
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7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | WebAssign
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A local television station plans to drop four Friday evening programs at the end of the season. Steve Botuchis, the station manager, developed a list of six potential replacement programs. Estimates of the advertising revenue ($) 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---
5. [–/0.76 Points] ASWMSCI15 6.E.019.DETAILS MY NOTES ASK YOUR TEACHER
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | WebAssign
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8:00–8:30 p.m. ---Select---
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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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ℹ
6. [–/0.76 Points] ASWMSCI15 6.E.027.DETAILS MY NOTES ASK YOUR TEACHER
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | 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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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 constraints are of the ≥ form.
All decision variable values are either 0 or 1.
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ℹ
7. [–/0.76 Points] ASWMSCI15 6.E.029.DETAILS MY NOTES ASK YOUR TEACHER
8. [–/0.76 Points] CAMMIMS16 6.TB.032.DETAILS MY NOTES ASK YOUR TEACHER
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | 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 3
2 to 5 6
3 to 4 4
3 to 5 6
4 to 6 7
5 to 6 2
Draw the network for this problem.
9. [–/0.88 Points] CAMMIMS16 6.TB.060.DETAILS
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ℹ
ℹ
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | 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
Node 3 Flows
ℹ
ℹ
ij
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | WebAssign
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Node 4 Flows
Node 5 Flows
Node 6 Flows
x > 0 for all i and j
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ij
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | 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 + 2x + 4x + 8x + 11x + 9x13 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
10. [–/0.76 Points] CAMMIMS16 6.TB.050.DETAILS
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ℹ
ℹ
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | WebAssign
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ℹ
ℹ
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | WebAssign
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The assignment problem constraint x + x + x + x ≤ 1 means
agent 1 can be assigned to three tasks.
agent 3 can be assigned to one task.
there is no feasible solution.
a mixture of agents 1, 2, 3, and 4 will be assigned to tasks.
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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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31 32 33 34
11. [–/0.76 Points] CAMMIMS16 6.TB.033.DETAILS MY NOTES ASK YOUR TEACHER
12. [–/0.76 Points] CAMMIMS16 4.TB.030.DETAILS MY NOTES ASK YOUR TEACHER
7/11/23, 1:09 AM 407 Module 2: Quiz#2 - MNS407 Management Science, Summer 1 2023 | 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 11 10 6 2 36
Tirey Hall 11 10 1 7 9
Arena 16 15 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 4
2 0 0 9 0
3 0 0 0 7
Total Transportation Cost or Revenue is 385 Note: The Total Supply Exceeds The Todal Demand By 12
Origin Excess Supply
3 12
(b) How many chairs are moved from Baker to Business?
(c) How many chairs are moved from Tirey to Parsons?
13. [–/0.76 Points] CAMMIMS16 6.TB.052.DETAILS
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(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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