A school stall’s profit from selling $n$ gift packs is modelled by $$P=-2n^2+48n-160,$$ where&nbsp

Question

A school stall’s profit from selling $n$ gift packs is modelled by $$P=-2n^2+48n-160,$$ where $P$ is in dollars and $n$ is a whole number satisfying $0\leq n\leq24$. Complete the square. Find the greatest possible profit and the corresponding number of packs. Find all values of $n$ for which the profit is positive.

Accepted Answer

(a) $P=-2(n-12)^2+128$; (b) Maximum $\$128$ at $n=12$; (c) Positive profit for $n=5,6,\ldots,19$.

Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Solution:

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