Assignment:
Theoretically, any given production plant has an optimum output level. Suppose a certain production plant has annual fixed costs PC = $2.000,000. Variable cost VC is functionally related to annual output Q in a manner that can be described by the function VC = 512 + $0.005Q. Total annual cost is given by TC = FC + VC x 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' IQ; 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.
Provide complete and step by step solution for the question and show calculations and use formulas.