Tiny Toy
Given:
Plastic used for one unit of each is 1.5, 2.0 and 1.0 pounds.
Rubber for one unit of each toy is 0.5, 0.5 and 1.0 pounds.
Each tank uses 0.5 pounds of metal.
Each tank uses 0.6 pounds of metal
Weakly availability of plastic is 16,000 pounds
Weakly availability of metal is 9,000 pounds
Weakly availability of rubber is 5,000 pounds
The company allows no more than 10 hours a week for production.
Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2)
Minimize the under and over-utilization of the budget. Maximize available labor hour usage (priority #3).
Variables:
X1 = No. of tiny tanks produced
X 2= No. of tiny trunks produced
X3 = No. of turk tanks produced
Oi= Excess of right side of the goal with respect to the goal.
Ui = Deficit of the right side of the goal with respect to goal ‘i’ V i=1, 2, …, -6.
Objective function: Min (0.36401 + 0.18202 + 0.18203 + 0.09104 + 0.09105 + 0.09106)
Subject to: 1.5 X1 + 2.0 X2+ 1.0 X3+ U1 – 01=16000
0.5 x 1 + 0.5 x 2 + 1.0 x 3 + U3-03=5000
0.3 x 1 + 0.6 x 2 +0.0 x 3 + U2-02=9000
2.0 x 1 + 2.0 x 2 + 1.0 x 3 + U6 -06 =40
7.0 x 1 + 5.0 x 2 + 4.0 x 3 + U4-04=164000
7.0 x 1 + 5.0 x 2 + 4.0 x 3 + U5-05=164000
X1,X2,X3,Oi, Ui>0
