Question: Consider the following linear program: MIN 6 x 1 + 9 x 2 ($ cost) s.t. x 1 + 2 x 2 8 10 x

Consider the following linear program:

MIN

6x1 + 9x2 ($ cost)

s.t.

x1 + 2x2 8

10x1 + 7.5x2 30

x2 2

x1, x2 0

a.

What is the optimal solution including the optimal value of the objective function?

b.

Suppose the unit cost of x1 is decreased to $4. Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4?

c.

How much can the unit cost of x2 be decreased without concern for the optimal solution changing?

d.

If simultaneously the cost of x1 was raised to $7.5 and the cost of x2 was reduced to $6, would the current solution still remain optimal?

e.

If the right-hand side of constraint 3 is increased by 1, what will be the effect on the optimal solution?

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