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In: Statistics and Probability

10. The Wearever Carpet Company manufactures two brands of carpet—shag and sculptured—in 10-yard lots. It requires...

10. The Wearever Carpet Company manufactures two brands of carpet—shag and sculptured—in 10-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lot of sculptured 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 of 40 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag is more important than meeting demand for sculptured, by a ratio of 5 to 2.

(3) Limit production overtime to 20 hours.

a. Formulate a goal programming model to determine the amount of shag and sculptured carpet to produce to best meet the company’s goals.

b. Solve this model by using the computer.

Solutions

Expert Solution

(a) Goal programming model is following:

Decision variables: Let x1, x2 be the number (in 100 yard lots) of shag and scultured carpets to be produced.

di+, di- be the positive and begative deviation variables for i-th goal.

Objective: Min 3*(480/480)*d1- + 2*(5/7)*(480/40)*d2- + 2*(2/7)*(480/50)*d3- + d4+

s.t.

8x1 + 6x2 - d1+ + d1- = 480 (Not underutilize production capacity)

x1 - d2+ + d2- = 40 (satisfy demand for 40 lots of shag carpets)

x2 - d3+ + d3- = 50 (satisfy demand for 50 lots of sculptured carpets)

8x1 + 6x2 - d4+ + d4- = 480+20   (limit overtime production to 20 hours)

x1, x2, di+, di- >= 0

(b) Solution of the model using LINDO is following (in LINDO model, positive and negative deviation variables are written as dip (for di+) and din (for di-) respectively)

Optimal solution:

x1 = 40

x2 = 30

d1+ = 20

d3- = 20

all other deviation variables = 0

orchestra answered 1 year ago
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