Solve the following linear programming problem:
MAX 2X1 + 3X2 + 4.5X3 + 5.25X4
4X1 + 5X2 + 6X3 + 7X4 <= 39,000 [1]
X1 + 2X2 + 3X3 +X4<= 26,000 [2]
X1 + X3 + X4 <= 5,500 [3]
X1 + X2 + X3 <= 10,000 [4]
X1 - 0.5X2 = 0 [5]
X1,X2,X3 >=0
What are the optimal solution and the optimal value of the objective function?
Answer the following questions, Only Resolve if necessary,
a) If the profit in variable three is increased by 0.5 units, will this change the optimal solution? If so, what is the new optimal solution? Will this change the optimal value of the objective function? If so, by how much?
b) If the restriction for constraint [1] is reduced to 35000, will this change the optimal solution? Will this change the optimal value of the objective function? If so, by how much?
c) What will be the effect of increasing by 1000 resources to constraint [3]? Will it change the optimal value? Will it change the optimal value of the objective function? If so, by how much?
d) If the profit in variable four is increased by 1.5 units, are there other optimal solutions? Explain why or why not. If there is at least one other solution, find another solution.
e) If the profit in variable two is increased to 4, will this change the optimal solution? If so, what is the new optimal solution? Will this change the optimal value of the objective function? If so, by how much?