Question

In: Mechanical Engineering

Consider the TOYCO model given below: TOYCO Primal: max z=3x1+2x2+5x3 s.t. x1 + 2x2 + x3...

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 the three operations as bT = [460, 500, 400](the new right-hand-side vector). Use the post optimality analysis to determine the optimum solution.

b) Suppose that TOYCO adds a fourth operation with the operation times 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 find the new solution.

d) Suppose TOYCO wants to produce toy planes. It requires 3,2,4 minutes respectively on operations 1,2, and 3. Determine the optimal solution when the revenue per unit for toy planes is $10.

Expert Solution

samet mamat answered 1 year ago

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