Question

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.

Answer 1

The original solution is shown below

a)

Keeping C2 (coefficient of X2) fixed at 1, the range of feasibility for C1 is 0 to 2 to infinity.

b)

Keeping C1 (coefficient of X1) fixed at 2, the range of feasibility for C2 is 0 to 1.

c)

The updated solution is shown below

The values are x1 = 100, x2 = 200 and obj func = 500

d)

The updated solution is shown below

The binding constraint is constraint 1 and 2

e)

The shadow price for each constraint is -4,-1, and 0