3. Ariel's company uses two factors of production: work [L] and capital [K]. The marginal productivity of Lis ngL = LIISKL'Z and uses a fixed amount of capital, K = 4. The board of directors of the company has decided to set a target profit {profit} of rt = 500. The prices of the factors of production labor and capital are, respectively, wL = 1 and 535. = 2 and the price ofthe product is P = 5. a. How much of Lwill be used and how much will be produced? b. Does production that maximizes profit meet the objective? Is this goal realistic? c. If the productivity of labor changes to ngL = fl; 333K What would be the quantity demanded of L and the quantity of production that maximizes benets, for K=4? d. Find the short-run cost curve for K=4; and the curves of Average Cost {CMe}, Marginal Cost {MC} and Average Variable Cost (CVMel