Consider a price-taking firm with production function q = q(K,L,F) = 10 K 1/4L 1/4F 1/2 in the short run: F is an input that is fixed at f = 16, and K and L are variable. The price of F is 1, the price of K is v, the price of L is w, and the price of output is P. By following the steps outlined below, you will solve for the firm's maximal profit without first solving for the cost functions. Note how the fixed costs do not play any role in this process. a. Compute the firm's profits (K,L) as a function of input usage (so, without first solving for the supply function) b. Use your result from part a to set up the problem of choosing inputs to maximize profits. c. Demonstrate that the conditions that you get in part b show that each (variable) input should be used up to the point where the revenue of its marginal product equals its price. d. Demonstrate that the conditions that you get in part b can be used to show that the tangency condition (MRT S = w v ) must hold when inputs are chosen