\"border: 0px; height: 0px; margin: 0px; padding: 0px; width: 707px\"> Klein Ind

ID: 1188159 • Letter: #

Question

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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 o 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.

let the quantity to be produced is x for small, y for medium and z for big

.4x+.7y+.8z <= 23400,

.6x+1y+1.2z<=23,400,

1.4x+2.6y+3.1z <= 46800,

maximize profit (P) = 20.50X + 34 Y + 42Z

solving the eqn we get x=117000 y=234000 z=-234000

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