(Solution) - Theoretically any given production plant has an optimum output level -(2025 Original AI-Free Solution)

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Theoretically, any given production plant has an optimum output level. Suppose a certain production plant has annual fixed costs FC = $2,000,000. Variable cost VC is functionally 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 + 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/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.