Posted: March 16th, 2022

Here’s a little help with Week 2 homework; The first three problems are from Tuesday’s Session

Here’s a little help with Week 2 homework; The first three problems are from Tuesday’s Session (3). See the Excel examples on tabs 5,6,7. Remember you can delete middle rows and columns from the examples to fit these problems. Do make sure they are from the middle of the array, not the ends.

First is a Make/Buy problem. It is a 6 by 6 problem. See pages 153-156. Use SOLVER here.

Second is a Production Scheduling problem. It is a 10 by 12 problem. See pages 157-163. us SOLVER here.

Third is a product mix. It is a 3 by 3 problem. problem. See pages 163-164. Write Equations only.

Instructions

The way that you write your answers matters! Syntax matters! Before you take this homework, be sure that you have successfully completed the “Getting Started in Web Assign for Mathematics” quiz this week. This quiz provides 2 bonus points that can be used during the course, and, most importantly, makes it clear how to provide answers that the homework and quizzes understand.

Description

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.

1.

A linear programming computer package is needed.

Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec’s production schedule calls for 5,500 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.

Component

Manufacturing Cost

Purchase Cost

Frame

$39.00

$52.00

Support

$12.50

$16.00

Strap

$7.50

$8.50

Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows.

Component

Department

Cutting

Milling

Shaping

Frame

3.5

2.2

3.1

Support

1.3

1.7

2.6

Strap

0.8

—

1.7

Capacity (hours)

350

420

680

(a)

Formulate and solve a linear programming model for this make-or-buy application. (Let FM = number of frames manufactured, FP = number of frames purchased, SM = number of supports manufactured, SP = number of supports purchased, TM = number of straps manufactured, and TP = number of straps purchased. Express time in minutes per unit.)

Min

Cutting constraint

Milling constraint

Shaping constraint

Frame constraint

Support constraint

Strap constraint

FM, FP, SM, SP, TM, TP ≥ 0

How many of each component should be manufactured and how many should be purchased? (Round your answers to the nearest whole number.)

(FM, FP, SM, SP, TM, TP) =

(b)

What is the total cost (in $) of the manufacturing and purchasing plan?

$

(c)

How many hours of production time are used in each department? (Round your answers to two decimal places.)

Cutting hrs

Milling hrs

Shaping hrs

(d)

How much (in $) should Frandec be willing to pay for an additional hour of time in the shaping department?

$

(e)

Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its position by pursuing this opportunity? Why or why not? (Round your answer to three decimal places.)

. The reduced cost of indicates that the solution be improved.

2.

A linear programming computer package is needed.

EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 9,000 windows in inventory. EZ-Windows’ management team would like to develop a production schedule for the next three months. A smooth production schedule is obviously desirable because it maintains the current workforce and provides a similar month-to-month operation. However, given the sales forecasts, the production capacities, and the storage capabilities as shown, the management team does not think a smooth production schedule with the same production quantity each month possible.

February

March

April

Sales forecast

15,000

16,500

20,000

Production capacity

14,000

14,000

18,000

Storage capacity

6,000

6,000

6,000

The company’s cost accounting department estimates that increasing production by one window from one month to the next will increase total costs by $1.00 for each unit increase in the production level. In addition, decreasing production by one unit from one month to the next will increase total costs by $0.65 for each unit decrease in the production level. Ignoring production and inventory carrying costs, formulate a linear programming model that will minimize the cost of changing production levels while still satisfying the monthly sales forecasts. (Let F = number of windows manufactured in February, M = number of windows manufactured in March, A = number of windows manufactured in April, I1 = increase in production level necessary during month 1, I2 = increase in production level necessary during month 2, I3 = increase in production level necessary during month 3, D1 = decrease in production level necessary during month 1, D2 = decrease in production level necessary during month 2, D3 = decrease in production level necessary during month 3, s1 = ending inventory in month 1, s2 = ending inventory in month 2, and s3 = ending inventory in month 3.)

Min

s.t.February Demand

March Demand

April Demand

Change in February Production

Change in March Production

Change in April Production

February Production Capacity

March Production Capacity

April Production Capacity

February Storage Capacity

March Storage Capacity

April Storage Capacity

Find the optimal solution.

(F, M, A, I1, I2, I3, D1, D2, D3, s1, s2, s3) =

Cost = $

·

·

3.

The Ace Manufacturing Company has orders for three similar products.

Product

Orders (units)

AA

1,800

BB

400

CC

1,400

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)

11

1,700

22

1,400

33

800

Machine

Product

1

2

3

A

$1.00

$1.30

$1.10

B

$1.20

$1.40

$1.00

C

$0.90

$1.20

$1.20

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

(a)

Show the linear programming formulation. (Let xA1 be the number of units of product A produced by machine 1,

xij

be the number of units of product i produced by machine j, etc.)

Min

s.t.Machine 1 Capacity

Machine 2 Capacity

Machine 3 Capacity

Product A Orders

Product B Orders

Product C Orders

xij ≥ 0 for all i, j.

(b)

Show the production schedule.

(xA1, xA2, xA3, xB1, xB2, xB3, xC1, xC2, xC3) =

(c)

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

Total = $

4.

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

Jackson1

10

16

32

Ellis2

14

22

40

Smith3

22

24

34

(a)

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

This answer has not been graded yet.

(b)

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

Min

s.t.Jackson

Ellis

Smith

Client 1

Client 2

Client 3

xij ≥ 0 for all i, j.

Solve.

Relationship

Assignment

Time (days)

x11

x12

x13

x21

x22

x23

x31

x32

x33

What is the total time required (in days)?

days

5.

Consider the following network representation of a transportation problem.

Diagram Description automatically generated

A network diagram between five locations is shown. The left-hand side of the graph is labeled “Supplies” and lists Jefferson City and Omaha. The right-hand side of the graph is labeled “Demands” and lists Des Moines, Kansas City, and St. Louis. Lines are shown between various locations. The following list contains the numbers placed on the graph.

· Jefferson City: 45

· Omaha: 40

· Des Moines: 20

· Kansas City: 15

· St. Louis: 50

· Jefferson City–Des Moines: 16

· Jefferson City–Kansas City: 9

· Jefferson City–St. Louis: 8

· Omaha–Des Moines: 8

· Omaha–Kansas City: 10

· Omaha–St. Louis: 23

The supplies, demands, and transportation costs per unit are shown on the network.

(a)

Develop a linear programming model for this problem; be sure to define the variables in your model.

Let

· x11 = amount shipped from Jefferson City to Des Moines

· x12 = amount shipped from Jefferson City to Kansas City

· x13 = amount shipped from Jefferson City to St. Louis

· x21 = amount shipped from Omaha to Des Moines

· x22 = amount shipped from Omaha to Kansas City

· x23 = amount shipped from Omaha to St. Louis

Min

x11

+

x12

+

x13

+

x21

+

x22

+

x23

s.t.

x11

+

x12

+

x13

≤

x21

+

x22

+

x23

≤

x11

+

x21

=

x12

+

x22

=

x13

+

x23

=

x11, x12, x13, x21, x22, x23 ≥ 0

(b)

Solve the linear program to determine the optimal solution.

Amount

Cost

Jefferson City–Des Moines

Jefferson City–Kansas City

Jefferson City–St. Louis

Omaha–Des Moines

Omaha–Kansas City

Omaha–St. Louis

Total

6.

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 picture containing text, watch, different Description automatically generated

A network diagram between six parties, distributed across four columns, is shown. The left-most column contains node 1. The second column contains nodes 2 and 3. The third column contains nodes 4 and 5. The right-most column contains node 6. Lines are shown between various locations. The following list contains the numbers placed on the graph.

· 1–2: 35

· 1–3: 30

· 2–1: 35

· 2–3: 12

· 2–4: 18

· 2–6: 39

· 3–1: 30

· 3–2: 12

· 3–5: 15

· 4–2: 18

· 4–5: 12

· 4–6: 16

· 5–3: 15

· 5–4: 12

· 5–6: 30

· 6–2: 39

· 6–4: 16

· 6–5: 30

(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 xij, where each xij 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

Node 5 Flows

Node 6 Flows

For all xij = 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.)

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