Suppose that a firm faces the Cobb-Douglas production functi

Suppose that a firm faces the Cobb-Douglas production function Q=10L0.5K0.5. Suppose the total cost is TC = 40L + 250K.Calculate the cost-minimizing combination of L and K that would allow this firm to produce 100 units of output. How much does it cost the firm to produce 100 units of output?Given the level of capital found in part a, what is the equation for the short-run production function? Suppose the firm wanted to produce 120 units of output in the short run, how much labor would they hire? 120=40L+250KWhat is the equation for the firm’s short run cost function at the level of K found in part a (as a function of Q; C=f(Q))? What is the equation for the long run cost function (again, as a function of Q)?