Demand for a product is modeled by

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Demand for a product is modeled by q=400−2pq=400-2p, where pp is the price in dollars. Production cost is C(q)=0.5q2+1000C(q)=0.5q^{2}+1000. Determine the quantity qq that maximizes profit and state the corresponding maximum profit to the nearest dollar.

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