Question

Question:

The Wearever Carpet Company manufactures two brands of carpet, shag and sculptured, in 100-yard lots. It requires eight hours to produce one lot of shag carpet and six 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) Limit production overtime to 20 hours.

(3) Achieve product demand of forty 100-yard lots for shag and fifty 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.

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

(b) Solve this problem (i.e., all the decision variables including the deviational variables should be found) using graphical method. (can use excel solver!!)

Answer 1

(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