3. A firm has three types of wood products (X1, X2, X3) each requires (or potentially requires) four inputs: A B, C and D.

Input X1 X2 X3 Amount of input available

A 1 1 2 19

B 0.5 1 1.5 16

C 0 0.5 1 8

D 0 0 1 11

The profit contribution of each output is $14, $16.5 and $30.5, respectively.

a. The company's objective is to choose the product mix that maximizes its profit. Write out the objective function and the constraints.

b. Find the profit-maximizing solution using EXCEL's Solver. Hand in copies of the answer report and the sensitivity report.

c. If you were to give it a two-dimensional interpretation (that is, think of a two product model on a graph), how would you interpret the "allowable increase" for the X3 coefficient?

d. Would it be worth for the firm to acquire one more unit of input A if it cost $10 to do so? Explain with reference to the shadow price.