Problem

Rewrite $P(q)=-3q^{2}+60q-100$ in vertex form by completing the square. State the admissible maximizing quantity and maximum profit, and explain the meaning of the vertex with units.

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P(q) = −3(q − 10)² + 200. The maximum occurs at admissible quantity q = 10 units and is $200, so the model predicts maximum profit of $200 at quantity 10.

P(q) = −3(q − 10)² + 200, so q = $10 and the maximum is 200 units. The input and output units are reversed.

P(q) = −3(q − 10)² + 200, so q = 10 units gives $200. The quantity is not checked against the nonnegative domain.

P(q) = −3(q − 10)² + 200, so the maximum profit is $200. The maximizing quantity and its domain status are not given.

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Rewrite \(P(q)=-3q^{2}+60q-100\) in vertex form by completing the square. State the admissible maximizing quantity and maximum profit, and explain the meaning of the vertex with units.

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