 Self Test Questions
Theory
1. What is goal programming? State clearly its assumptions.
2. Identify the major differences between linear programming and goal
programming.
3. State some problem areas in management where goal programming might
be applicable.
Practical
1. Company XYZ, produces two products. The maximum sales potential
for product 1 and product 2 are 30 units and 40 units respectively.
Write the goal constraints for achieving the sales goal by incorporating
the deviational variables.
2. An office equipment manufacturer produces two kinds of products,
chairs and lamps. Production of either a chair or lamp requires 1 hour
of production capacity in the plant. The plant has a maximum production
capacity of 10 hours per week. Because of the limited sales capacity,
the maximum number of chairs and lamps that can be sold are 6 and 8
per week, respectively. The gross margin from the sale of a chair is
Rs. 80 and Rs. 40 for a lamp.
The plant manager has set the following goals arranged in the order
of importance:
- He wants to avoid any underutilization of production capacity.
- He wants to sell as many chairs and lamps as possible. Since the
gross margin from the sale of chair is set a twice the amount of profit
from a lamp, he has twice as much desire to achieve the sales goal
for chairs as for lamps.
- He wants to minimize the overtime operation of the plant as much
as possible.
Formulate this as a goal programming problem and then solve by both
graphical and simplex method.
3. Minimize z = P1d1-
+ 2P2d2-
+ P2d3-
+ P3d1+
subject to
x1 + x2 + d1-
- d1+ = 45
x1 + d2-
= 25
x2 + d3-
= 35
x1, x2, d1-,
d2-, d3-,
d1+ ³ 0
4. Minimize z = P1d1-
+ 3P2d2-
+ P2d3-
+ P3d1+
subject to
x1 + x2 + d1-
- d1+ = 300
x1 + d2-
= 140
x2 + d3-
= 200
and x1, x2, d1-,
d2-, d3-,
d1+ ³ 0
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