Manufacturing profit curve

Secondary 2

TGM Original Questions

A manufacturer’s total profit, in dollars, from $x$ toys is $P=30x-180-\frac{x^2}{4}$, where $0\le x\le100$.

Find the missing table values $p,q$.
Plot the graph.
Use it or calculation to find
1. the profit for 45 toys,
2. the production levels giving $\$650$ profit,
3. the production level and total profit at the maximum, and the corresponding profit per toy, and
4. the profit for 6 toys and its meaning.

$x$	$0$	$10$	$20$	$30$	$40$	$50$	$60$	$70$	$80$	$90$	$100$
$P$	-$180$	$95$	$p$	$495$	$620$	$695$	$q$	$695$	$620$	$495$	$320$

Similar questions are unavailable for this question.

Answer:(a) $p=320,q=720$; (c)(i) $\(663.75$; (ii) $x\approx43.27,76.73$; (iii) $60$ toys, 720\) total, $\(12$ per toy; (iv) $-$9\), a $\$9$ loss.

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