Costs of Manufacturing Operations 3 = 3.12 Theoretically, any given production plant has an optimum output level. Suppose a cer- tain production plant has annual fixed costs FC $2,000,000. Variable cost VC is func- tionally related to annual output Q in a manner that can be described by the function VC $12+ $0.005Q. Total annual cost is given by TC-FC+ VCX Q. 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.