A firm manufactures a product, called wuab, out of two inputs, raw material and labor. The firm has a patent on this product. Letting qstand for the amount of wuabproduced, mbe the amount of raw material and lthe amount of labor input, the firm's isoquant is given by q = m^0.5 l^0.5. The price of a unit of raw material is 1, and the price of a unit of labor is 4. In addition, the firm must pay two administrative permits to produce wuab, which cost 300 and 800, respectively, per production period, regardless of how much wuabit produces. The (inverse) demand function for wuab is P = 12- (q/2000) where q is the number of wuab produced.

a)First, find the total cost function for this firm, TC(q).And, in particular, find the value of TC(1000).

b)Then, find the profit-maximizing production level and the price. Explain.