Home furnishings for department stores. Planning is underway for the production

Question

Home furnishings for department stores. Planning is underway for the production of items in the "flower" fabric pattern during the next production period. Inventory of the flower fabric is 3000 yards. Five hundred hours of production time have been scheduled. Four hundred units of packaging material are available. Each of these values can be adjusted through overtime or extra purchases. Home furnishings would like to achieve a profit of $3200. avoid purchasing more fabric or packaging material, and use all of the hours scheduled. Give the goal programming model. Set up the LP Model.

Explanation / Answer

LP Model:

Decision Variables: a, b, c as the number of units of bedspreads, curtains, and dust ruffles produced.

Objective function: Value of (12 a+ 10 b+ 8 c) = 3200

Constraints:

7a+4b+9c<=3000 (fabric constraint)

1.5a+2b+0.5c = 500 (time constraint)

3a+2b+1c<=400 (packaging material constraint)

a,b,c >=0, int

Goal Programming Model:

since all the constraints cannot be met in the above LP model and when solved we do get a uniques asolution that fulfills the constraints, we use goal programming:

Solving the above LP we get:

7a+4b+9c + U1 - E1<=3000 (fabric constraint)

1.5a+2b+0.5c + U2 - E2 = 500 (time constraint)

3a+2b+1c + U3 - E3<=400 (packaging material constraint)

where, Ui = amount by which the LHS falls short of the RHS value, and

Ei =amount by which the LHS exceeds the RHS value

12 a+ 10 b+ 8 c = 3200

a,b,c, Ui, Ei >=0, int

Objective Function:

Minimize (Ui + Ei)

Bedspread Curtains Dust Ruffle total max 0 42.86 314.29 LHS RHS Fabric Required (yds) 7 4 9 3000 <= 3000 Time required (hrs) 1.5 2 0.5 242.8571 >= 500 Packaging Material 3 2 1 400 <= 400 Profit 12 10 8 2942.857 = 3200

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