An integer setting cannot use a fractional optimum

9 written marks

A school-fair model gives the surplus, in dollars, as \(P(n)=-2n^2+38n-120\), where \(n\) is an integer number of bundles and \(0\le n\le18\).

1. Find all values of \(n\) for which the surplus is positive.

   [3]

2. Find all values of \(n\) for which the surplus is at least 40 dollars.

   [3]

3. Find the greatest possible surplus, and every integer \(n\) that attains it.

   [3]

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