Assume a profit-maximizing firm produces its output according to this response function, Y = 35+ 120x + 150x2 -1.5x1-2.5x Assume also that this firm receives $2.00 per unit for what it sells and it pays $64.00 per unit for the input X and $48.00 per unit for input x2. Using this response function and price information: a. (10 points) Derive this firm's optimal input levels. (4 points) Verify these critical values satisfy the second order conditions for a profit maximum. points) Derive this firm's optimal output level. Doints) Verify that your solution satisfies the Total Condition. Dints) Derive this firm's maximum profit. (17 points) Using the production function and input and output price information from Question 5 above, suppose that the firm now faces a budget constraint that limits the amounts of the two variable inputs it can purchase. Specifically, assume the firm has only $3,000 available to purchase its variable inputs. How much of each input will the firm use to maximize its output, given the budget constraint? How much will it produce? What will its profit be at that point? Interpret the Lagrangean multiplier calculated. (8 points) Illustrate graphically, using ridgelines and psuedoscale lines, the solution to the budget-constrained output maximization problem from Question 6, as compared to the optimal solution derived in Question 5. Explain your graph.