Question

For the given LP formulation, find the optimal solution using excel solver.
Max(Z) = 5X1 + 8X2

Constraints :

2X1 + 4X2 <= 40

6X1 + 3X2 <= 42

X1 >= 3

X1,X2 >= 0
(a) Insert below a screenshot of the excel solver with final answers in it.

(b) Write clearly which constraints are binding and which are non binding.

(c) How much change can we make in the first constraint without changing the optimal solution for Z.

(d) (2 points) Can we increase the right hand side value of the constraint (X1 >= 3) to 5 to obtain the same optimal value of Z? Give reason for your answer?

Answer 1

a)

Formula used

Solver window input

Sensitivity report

b)

Following constraints are binding :

6X1 + 3X2 <= 42
X1 >= 3

Non-binding constraints :

2X1 + 4X2 <= 40

c)

We can decrease RHS of 2X1 + 4X2 <= 40 by 2 and increase upto infinity without changing the optimal solution for Z. because there is a slack of 2 unit in the constraint

d)

No optimal value of Z will change as constraint (X1 >= 3) is binding and has shadow price of -11 which is again valid till increase of RHS upto 7. Hence increasing right hand side value to 5 will decrease Z to 79+2*(-11) = 57