Question

The Wearever Carpet Company manufactures two brands of carpets-shag and sculptured-in 100 yard lots. It requires 8 hours to produce one lot o shag carpet and 6 hours to produce one lot of sculpture carpet. The company has the following production goals, in prioritized order:

1) Do Not underutilize production capacity, which is 480 hours.

2) Achieve product demand for shag is more important than meeting demand for sculptured, by a ration of 5 to 2. 3) Limit production overtime to 20 hours

Solve:

a) Fromulate a Goal Programming Model to determine teh amount of shag and sculptured carpet to produce the best meet the company's goals.

b) Solve his model by using the computer (Excel and Solver)

c) include a separate sheet with your goal programming model: define each regular decision variable and deviational variable explicitly in your model, and indicate which goal each of your constraints refers to

Answer 1

a) Goal programming model is following

Standard variables: Let S and C be the number of 100-yard lots of Shag (S) and Sculpted (C) carpets to be produced. O be the number of overtime hours to be used

Deviation variables: Let djp and djn be the positive and negative deviation variables respectively for jth goal

Min 3*d1n + 2*2*(5/7)*d2n + 2*2*(2/7)*d3n + 1*d4p

8S+6C-O <= 480

goal 1: 8S+6C-O-d1p+d1n = 480   

goal 2a: S - d2p + d2n = 40

goal 2b: C - d3p + d3n = 50

goal 3: O - d4p + d4n = 20

All variables >= 0

b) Solution using Excel Solver is following:

c) Optimal solution:

Values of Decision variables

S = 40

C = 30

O = 20 hours

Deviation variables:

d3- = 20