Consider the TOYCO model given below:
TOYCO Primal:
max z=3x1+2x2+5x3
s.t.
x1 + 2x2 + x3 ? 430 (Operation 1)
3x1 + 2x3 ? 460 (Operation 2)
x1 + 4x2 ? 420 (Opeartion 3 )
x1, x2, x3 ?0
Optimal tableau is given below:
| basic | x1 | x2 | x3 | x4 | x5 | x6 | solution |
| z | 4 | 0 | 0 | 1 | 2 | 0 | 1350 |
| x2 | -1/4 | 1 | 0 | 1/2 | -1/4 | 0 | 100 |
| x3 | 3/2 | 0 | 1 | 0 | 1/2 | 0 | 230 |
| x6 | 2 | 0 | 0 | -2 | 1 | 1 | 20 |
a) Suppose that TOYCO wants to change the capacities of thethree operations as bT = [460, 500, 400](the new right-hand-sidevector). Use the post optimality analysis to determine the optimumsolution.
b) Suppose that TOYCO adds a fourth operation with the operationtimes of 4, 1, and 2 minutes for product 1, 2, and 3 respectively.Assume that the capacity of the fourth operation is 548 minutes.Determine the new optimal solution for this case.
c) Suppose the objective function is changed to z = 3x1 + 6x2 +x3. If the solution changes, use the post-optimal analysis to findthe new solution.
d) Suppose TOYCO wants to produce toy planes. It requires 3,2,4minutes respectively on operations 1,2, and 3. Determine theoptimal solution when the revenue per unit for toy planes is$10.
