2. You are hired to consult for a firm. They want to know how much of each of sers goodie they should produce. They sell good X in a monopolistically competitive market with the nese demand curve P, = 500-15X . They sell good Y in a competitive market with a market price of ?= $30 The firm's cost function is C(X, Y) = 7X2 + 4XY + 2Y2 A. What is the firm's total revenue from selling BOTH goods? Assume you sellunits of pont & and Y units of good Y. Assume a max exists. B. Write the firm's profit function in terms of X and Y. C. Find the First Order Conditions (FOC's) and set each equal to zero. D. Use the FOC's so solve for the number of units of X* and " that maximize profits. E. (On your own): Write our the equations for MR., MR, , MC., MC, . Them giug in the \\" and Clearly identify each step (A, B, C, D) and your answer to each part.3. Afirm produces output for sale | N a competitive market. The price of output is Pq = 50. The firm hires labor (at $10 per unit) and capital (S5 per unit). The firm's production function is Q = 025 go7s Find the ratio of Labor and Capital that maximizes profit. Specifically, find K = (?) L. Find the number for \"?\" Set up the profit function. Find the FOC's wrt L & K. Then using each FOC, set BOTH to the same value. (hint: try to solve both FOC's so the right side is1). Move everything else to the left side. Then set the two left sides equal and solve for K as a function of L. This ratio is important,. 2" method: Compute MP_ and MPy, then find MRTS = MP. / MP, = w/r 4. A firm produces output for sale in a competitive market. The price of output is PQ = P. The firm hires labor (at $w per unit) and capital ($r per unit). The firm's production function is Q = L0.25 K0.75 The problem is the general situation for the problem above, using P, w, and r as the prices of output and inputs. The Cobb-Douglas production function is the same. Your answers will include P, w, and r as parameters. A. Write the function for Profit. B. Find the FOC's wrt L and K and set equal to zero. C. Try to solve for K as a function of L. This will include P, w, and r