Question: 4. Consider the following linear program: MAX 3 x 1 + 4 x 2 ($ Profit) s.t. x 1 + 3 x 2 12 2

4. Consider the following linear program:

MAX

3x1 + 4x2 ($ Profit)

s.t.

x1 + 3x2 12

2x1 + x 2 8

x1 3

x1, x2 0

a.

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

b.

Suppose the profit on x1 is increased to $7. Is the above solution still optimal? What is the value of the objective function when this unit profit is increased to $7?

c.

If the unit profit on x2 was $10 instead of $4, would the optimal solution change?

d.

If simultaneously the profit on x1 was raised to $5.5 and the profit on x2 was reduced to $3, would the current solution still remain optimal?

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