# KLEIN INDUSTRIES OPTIMIZATION MODEL

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**This is an Excel and a APA paper report explaining the “solver process”.**

**APA paper to explain all your findings together with your Excel Worksheet to demonstrate you have set up the Solver correctly. In the paper, you also need to explain how you set up the LP model to solve this case study.**

Klein Industries manufactures three types of portable air compressors: small, medium, and large, which have unit profits of $20.50, $34.00, and $42.00, respectively. The projected monthly sales are:

Small Medium Large

Minimum 14,000 6,200 2,600

Maximum 21,000 12,500 4,200

The production process consists of three primary activities: bending and forming, welding, and painting. The amount of time in minutes needed to process each product in each department is shown below:

Small Medium Large Available Time

Bending/forming 0.4 0.7 0.8 23,400

Welding 0.6 1.0 1.2 23,400

Painting 1.4 2.6 3.1 46,800

How many of each type of air compressor should the company produce to maximize profit?

a. Formulate and solve a linear optimization model using the auxiliary variable cells method and write a short memo to the production manager explaining the sensitivity information.

b. Solve the model without the auxiliary variables and explain the relationship between the reduced costs and the shadow prices found in part a.

**Instruction:**

There is no external data set provided. Use what is given by the problem. **You need to submit a formal APA paper to explain all your findings together with your Excel Worksheet to demonstrate you have set up the Solver correctly. In the paper, you also need to explain how you set up the LP model to solve this case study.**

13-7. Klein Industries manufactures three types of portable air compressors: small, medium, and large, which have unit profits of $20.50, $34.00, and $42.00, respectively. The projected monthly sales are:

Small Medium Large

Minimum 14,000 6,200 2,600

Maximum 21,000 12,500 4,200

The production process consists of three primary activities: bending and forming, welding, and painting. The amount of time in minutes needed to process each product in each department is shown below:

Small Medium Large Available Time Bending/forming 0.4 0.7 0.8 23,400

Welding 0.6 1.0 1.2 23,400

Painting 1.4 2.6 3.1 46,800

How many of each type of air compressor should the company produce to maximize profit?

a. Formulate and solve a linear optimization model using the auxiliary variable cells method and write a short memo to the production manager explaining the sensitivity information.

b. Solve the model without the auxiliary variables and explain the relationship between the reduced costs and the shadow prices found in part a.

Ins

truction:

There is no external data set provided. Use what is given by the problem.

You need to submit a formal APA paper to explain all your findings

together with your Excel Worksheet to demonstrate you have set up

th

e Solver correctly. In the paper, you also need to explain how you

set up the LP model to solve this case study.

13

–

7.

Klein Industries manufactures three types of portable

air

compressors: small, medium, and large, which have

unit profits of $20.50,

$

34.00, and $42.00, respectively.

The projected monthly sales are:

Small

Medium

Large

Minimum

14,000

6,200

2,600

Maximum

21,000

12,500

4,200

The production process consists of three primary activities: bending and

form

ing, welding, and painting. The amount of time in minutes needed to

process each product in each department is shown below:

Small

Medium

Large

Available Time

Bending/forming

0.4

0.7

0.8

23

,400

Welding

0.6

1.0

1.2

23,400

Painting

1.4

2.6

3.1

46,800

How many of each type of air compressor should the company produce to

maximize profit?

a.

Formulate and solve a linear optimization model using the auxiliary

variable cells method and write a short memo to the production manager

explaining the sensitivi

ty information.

b.

Solve the model without the auxiliary variables and explain the

relationship between the reduced costs and the shadow prices found in part

a.

Instruction:

There is no external data set provided. Use what is given by the problem.

You need to submit a formal APA paper to explain all your findings

together with your Excel Worksheet to demonstrate you have set up

the Solver correctly. In the paper, you also need to explain how you

set up the LP model to solve this case study.

13-7. Klein Industries manufactures three types of portable air

compressors: small, medium, and large, which have unit profits of $20.50,

$34.00, and $42.00, respectively. The projected monthly sales are:

Small Medium Large

Minimum 14,000 6,200 2,600

Maximum 21,000 12,500 4,200

The production process consists of three primary activities: bending and

forming, welding, and painting. The amount of time in minutes needed to

process each product in each department is shown below:

Small Medium Large Available Time

Bending/forming 0.4 0.7 0.8 23,400

Welding 0.6 1.0 1.2 23,400

Painting 1.4 2.6 3.1 46,800

How many of each type of air compressor should the company produce to

maximize profit?

a. Formulate and solve a linear optimization model using the auxiliary

variable cells method and write a short memo to the production manager

explaining the sensitivity information.

b. Solve the model without the auxiliary variables and explain the

relationship between the reduced costs and the shadow prices found in part

a.