1 1. Consider a firm with a Cobb-Douglas production Q(K,L) : 410/3ng where K is units of capital, L is units of labor, and (1 represents output. Assume the firm faces input prices of r = $10 per unit of capital and w: 57 per unit of labor. e. Solve the firm's cost-minimization problem (CM P}, to obtain the combination of inputs (capital and labor) that minimizes the firm's cost of producing a given amount of output, 0. Use those results to find the firm's total cost function. This is the firm's long-run cost function as all inputs can be varied. Find the firm's marginal cost (MC) function, and its average cost (AC) function. Interpret. Assume now that the amount of capital is fixed at E : 3 units. Solve the firm's cost- minimization problem again to find the amount of labor used that now minimizes the firm's cost. Finally, use the results from (d) to find the firm's short-run cost function (as K is fixed)