Answer
There are 50 ovens must be manufactured in a given week to generate a profit of $1250.
Work Step by Step
$P=\frac{1}{10}x(300-x)=30x-\frac{1}{10}x^{2}$, $0\leq x \leq200$
$P=1250$
Then $30x-\frac{1}{10}x^{2}=1250$
$-\frac{1}{10}x^{2}+30x-1250=0$
$x=\frac{-30+\sqrt (30^{2}-4\times(-\frac{1}{10})\times(-1250)}{2\times(-\frac{1}{10})}=\frac{-30+\sqrt 400}{(-\frac{2}{10})}=50$
or $x=\frac{-30-\sqrt (30^{2}-4\times(-\frac{1}{10})\times(-1250)}{2\times(-\frac{1}{10})}=\frac{-30-\sqrt 400}{(-\frac{2}{10})}=250$
Because $0\leq x \leq200$, $x=50$
So there are 50 ovens must be manufactured in a given week to generate a profit of $1250.
