Question

ABC a manufacturer of microwaves sells three popular models. The demand for models A, B, and C is limited to 800, 400, and 600 per week respectively. ABC has a weekly labor capacity of 1,800 hours, with each model A, B, and C taking 1, 1.5 and 2 hours respectively to produce. The models A, B, and C use 4, 3, and 5 processors respectively. ABC can get a supply of maximum 4000 processors each week. Each model A, B, and C yields a profit of $20, $30 and 40 respectively. ABC has the following goals for the company (1). Maximize profit, (2). Maximize number of microwaves produced. a) Formulate this Goal programming problem. b) Solve the LP problems to maximize each goal. Show both solutions and objective functions. c) Solve the goal programming problem to minimize the maximum % deviation from each goal. Show the target for each goal, the % deviation from each goal, and your solution. d) What will be new solution if Goal # 1 was twice as important as Goal # 2?

Answer 1

1)

Goal programming model is following:

Let A, B, C be the number of three models to be produced

pi, ni be the positive and negative deviation variables for goal i

MIN n1 + n2

s.t.

1A+1.5B+2C <= 1800 (weekly labor capacity)

4A+3B+5C <= 4000   (maximum supply of processors each week)

A <= 800 (Demand of model A)

B <= 400 (Demand of model B)

C <= 600 (Demand of model C)

Goal 1: 20A+30B+40C-p1+n1 = 52000 (maximize profit)

Goal 2: 1A+1B+1C-p2+n2 = 1800 (maximize number of microwaves produced)

A, B, C, pi, ni >= 0

------------------------------------------------------------------------

b)

Solution of the LP model using LINDO is as follows:

RESULT:

Objective function value = 18,440