3. A firm has three types of wood products (X₁, X2, X3) each requires (or potentially requires) four inputs: A B, C and D. The profit contribution of each output is $20, $27 and $34.5, 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.

Fig: 1