Consider a two input firm which faces an aggregate technology for perfect compliments of y=min(3x1,x2). a. Plot isoquants for y=3,6 and 9 b. What are the returns of scale for this production function? c. For all possible prices on output, p, and on inputs, w1 and w2, are their price combinations for which a profit maximizing firm would not be able to select a price maximizing quantity (or at least one greater than 0)? Give a restriction on prices such that a profit maximizing firm will be able to solve their problem. What are the solution(s) and level of profits for such a firm. d. Suppose we are looking to the solve the cost minimization for producing 3 units of output. Find x1 and x2 as a function of w1 and w2 as well as the level of cost for each price combination. Show graphically why your solution makes sense