Question: The binding constraints for this problem are the first and second. Min 2x1 + x2 s.t. x1 + x2 >=300 2x1 + x2 >=400 2x1

The binding constraints for this problem are the first and second.

Min

2x1 + x2

s.t.

x1 + x2 >=300

2x1 + x2 >=400

2x1 + 5x2 >=750

x1 , x2 >= 0

a.

Keeping c2 fixed at 1, over what range can c1 vary before there is a change in the optimal solution point?

b.

Keeping c1 fixed at 2, over what range can c2 vary before there is a change in the optimal solution point?

c.

If the objective function becomes Min 2x1 + 1.5x2, what will be the optimal values of x1, x2, and the objective function?

d.

If the objective function becomes Min 6x1 + 5x2, what constraints will be binding?

e.

Find the shadow price for each constraint in problem d.

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