Suppose a firm's production function is given by Q=F(L,K) = 5LK, where L is the amount of labor and K is the amount of capital. For this particular Cobb-Douglas production function, MRTS(L,K) = (K/L). The wage rate is $100 per unit of labor and the rental rate of capital is $50 per unit of capital.
Find:
a) The least-cost combination of capital and labor if the firm produces 1000 units of output
b) The short-run cost function if the firm currently uses 10 units of capital
c) The firm's long run cost function