1) A firm produces two outputs, X and Y, using three inputs, A, B, and C. Outputs X and Y sell for $4 and $6, respectively. Each unit of X requires 1 unit of A, 2 units of B, and 2 units of C to produce. Each unit of Y requires 2 units of A, 3 units of B, and 2 units of C to produce. The firm has 18 units of A, 36 units of B, and 24 units of C available. a) Solve the firm's profit maximization problem in Excel. What is the firm's optimal production plan and maximum profit? b) Draw a figure similar to that on slide 20 of the Chapter 8 Lecture Overheads illustrating the optimal solution, except draw only the single isoprofit line passing through the optimal production plan. c) What are the X and Y axis intercepts of the isoprofit line passing through the optimal production plan? d) What are the corner points of the feasible region? e) What are the shadow prices of inputs A, B, and C?