1.Theoretically, any given production plant has an optimum output level. Suppose a certain production plant has annual fixed costs = $2,000,000. Variable cost is functionally related to annual output Q in a manner that can be described by the function C_v = $12 + $0.005Q. Total annual cost is given by TC = C_f + C_vQ. The unit sales price for one production unit P = $250.

(a)Determine the value of Q that minimizes unit cost UC, where UC = TC/Q; and compute the annual profit earned by the plant at this quantity.

(b)Determine the value of Q that maximizes the annual profit earned by the plant; and compute the annual profit earned by the plant at this quantity