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MNS407 Management Science, Fall 2024

407 Module 2: Homework#2 (Homework) INSTRUCTOR

Vahid Keyhani National University, La Jolla CA

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QUESTION

POINTS

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SAT, NOV 9, 2024

11:59 PM PST

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This homework covers material in Chapters 4 and 6, and some questions require the use of Excel and Solver. You

have 5 attempts to get this right. Feel free to submit until you are satis�ed with the results. Do not forget to use the

practice button and help hints in the process.

Remember you have taken the "Getting Started in Web Assign for Mathematics" quiz in week one because the way

you write your answers matters for homework, quizzes, and the �nal. Be careful with syntax again.

Assignment Submission & Scoring

Assignment Submission

For this assignment, you submit answers by question parts. The number of

submissions remaining for each question part only changes if you submit

or change the answer.

Assignment Scoring

Your last submission is used for your score.

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11/3/24, 10:55 PM 407 Module 2: Homework#2 - MNS407 Management Science, Fall 2024 | WebAssign

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A linear programming computer package is needed.

Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3,300 bookshelf speakers and 4,100 floor speakers over the next two months, with the following delivery schedule.

Model Month 1 Month 2

Greenville estimates that the production time for each bookshelf model is 0.7 hours and the production time for each floor model is 1 hour. The raw material costs are $10 for each bookshelf model and $12 for each floor model. Labor costs are $22 per hour using regular production time and $33 using overtime. Greenville has up to 2400 hours of regular production time available each month and up to 1000 additional hours of overtime available each month. If production for either cabinet exceeds demand in month 1, the cabinets can be stored at a cost of $5 per cabinet. For each product, determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs. Round your answers to the nearest integer. (Let BaR = regular bookshelf units for month 1, BbR = regular bookshelf units for month 2, FaR = regular floor units for month 1, FbR = regular floor units for month 2, BaO = overtime bookshelf units for month 1, BbO = overtime bookshelf units for month 2, FaO = overtime floor units for month 1, and FbO = overtime floor units for month 2)

(BaR, BbR, FaR, FbR, BaO, BbO, FaO, FbO) =

Total Production Cost = $

268,320.00

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(Optional)

Bookshelf 2,100 1,200

Floor 1,500 2,600

3300,0,0,4100,0,0,0,0

1. [0/1.33 Points] ASWMSCI15 4.E.021.DETAILS MY NOTES PREVIOUS ANSWERS

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A linear programming computer package is needed.

Seastrand Oil Company produces two grades of gasoline: regular and high octane. Both gasolines are produced by blending two types of crude oil. Although both types of crude oil contain the two important ingredients required to produce both gasolines, the percentage of important ingredients in each type of crude oil differs, as does the cost per gallon. The percentage of ingredients A and B in each type of crude oil and the cost per gallon are shown.

Crude Oil Cost Ingredient A Ingredient B

Each gallon of regular gasoline must contain at least 40% of ingredient A, whereas each gallon of high octane can contain at most 50% of ingredient B. Daily demand for regular and high-octane gasoline is 1,000,000 and 700,000 gallons, respectively. How many gallons of each type of crude oil should be used in the two gasolines to satisfy daily demand at a minimum cost? (Round your answers to the nearest gallon.)

gallons of crude 1 used to produce regular gal

gallons of crude 1 used to produce high-octane gal

gallons of crude 2 used to produce regular gal

gallons of crude 2 used to produce high-octane gal

What is the total minimum cost (in $) for the gallons? (Round your answer to the nearest dollar.)

$

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(Optional)

1 $0.20 20% 60%†

2 $0.25 50% 30%

2. [–/1.35 Points] ASWMSCI15 4.E.015.DETAILS MY NOTES PRACTICE ANOTHER

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Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows.

Project Leader Client

1 2 3

(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)

Choose File No file chosen

This answer has not been graded yet.

(b) Formulate the problem as a linear program. (Express your answers in the form x where x represents the completion time from leader i to client j.)

Min

s.t. Jackson

Ellis

Smith

Client 1

Jackson 1 10 16 32

Ellis 2 14 22 40

Smith 3 22 24 34

ij ij

3. [–/1.33 Points] ASWMSCI15 6.E.017.DETAILS MY NOTES

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Client 2

Client 3

Solve.

Relationship Assignment Time (days)

What is the total time required (in days)?

days

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(Optional)

x ≥ 0 for all i, j.ij

x11

x12

x13

x21

x22

x23

x31

x32

x33

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The Ace Manufacturing Company has orders for three similar products.

Product Orders (units)

Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below.

Machine Capacity (units)

Machine

Product 1 2 3

A

B

C

Use the transportation model to develop the minimum cost production schedule for the products and machines.

(a) Show the linear programming formulation. (Let x be the number of units of product A produced by machine 1, be the number of units of product i produced by machine j, etc.)

Min

s.t. Machine 1 Capacity

A A 2,200

B B 500

C C 1,300

1 1 1,500

2 2 1,500

3 3 1,200

$1.00 $1.30 $1.10

$1.20 $1.40 $1.00

$0.90 $1.20 $1.20

A1 xij

4. [–/1.33 Points] ASWMSCI15 6.E.009.DETAILS MY NOTES PRACTICE ANOTHER

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Machine 2 Capacity

Machine 3 Capacity

Product A Orders

Product B Orders

Product C Orders

x ≥ 0 for all i, j.

(b) Show the production schedule.

(c) Determine the cost (in dollars) of the production schedule.

Total = $

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(Optional)

ij

(x , x , x , x , x , x , x , x , x ) =

A1 A2 A3 B1 B2 B3 C1 C2 C3

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Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD's business involves rapid delivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveries anywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a guaranteed delivery time. The following network shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations.

(a) Develop a linear programming model that can be used to find the minimum time required to make a delivery from location 1 to location 6. (Express your answers in the form x , where each x

represents the arc from node i to node j as either 1 or 0.)

Min

s.t. Node 1 Flows

Node 2 Flows

Node 3 Flows

Node 4 Flows

ℹ

ij ij

5. [–/1.33 Points] ASWMSCI15 6.E.025.DETAILS MY NOTES

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Node 5 Flows

Node 6 Flows

For all x = 0, 1.

(b) How long (in minutes) does it take to make a delivery from location 1 to location 6? (Round your answer to the nearest whole number.)

min

(c) Assume that it is now 1:00 p.m. and that CARD just received a request for a pickup at location 1. The closest CARD courier is 8 minutes away from location 1. If CARD provides a 20% safety margin in guaranteeing a delivery time, what is the minimum guaranteed delivery time if the package picked up at location 1 is to be delivered to location 6? (Enter your answer in standard time. Round your answer to the nearest minute.)

: p.m.

Show My Work

(Optional)

ij

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For the following highway network system, determine the maximal flow in vehicles per hour.

What is the current flow capacity (in vehicles per hour) of the highway?

vehicles per hour

The highway commission is considering adding segment 3-4 to permit a flow of 2,000 vehicles per hour or, at an additional cost, a flow of 3,000 vehicles per hour. What is your recommendation for the proposed segment 3-4 of the highway network?

Add segment 3-4 with capacity 2,000 vehicles per hour.

Add segment 3-4 with capacity 3,000 vehicles per hour.

Do not add segment 3-4.

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ℹ

6. [–/1.33 Points] ASWMSCI15 6.E.033.DETAILS MY NOTES

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