Microecon material. Thanks in advance.

1. Production and Cost Functions (30 points) Suppose a rm in a competitive industry has a production lnction given by Q = L'3KO'5 and input prices are W = 6 and r = 10 for L and K respectively. a) Derive the marginal product of labor MPL and average product of labor APL for the rm when capital (K) is xed at 100 in the short run. 1)) In the long run, when both L and K are variable, derive the cost function C (Q) for the rm. 0) Following b), if the rm is using 50 units of capital (K) in production, how much labor (L) should be employed to minimize costs. d) Does the production mction (Q = LO'SKD'S) exhibit decreasing, constant, or increasing returns to scale? (Briey explain how you get the answer)