A rm produces output according to the following function: q = f[L, K) = L1/2 K1/3 The cost of labor is $9 per hour and the rental cost of capital is $4 per hour. 1] With the given prices, use the Lagrangian method to compute the optimal (cost minimizing) capital to labor ratio (K / L] for the rm. 2] Suppose the rm wishes to produce 7 2 units of output. How much capital and how much labor does the firm employ? 3] What is the total cost of producing 72 units of output? 4] Suppose that the rm suddenly decides to double the quantity of output but only has a day to complete the order. Therefore, in that time, the amount of capital is xed but labor hours are not. a) How much will it cost to produce 144 units of output? b] How much would it cost if the rm could also vary capital? Compute as well as providing a graph [isocost/isoquant] illustrating the optimal bundles