Question

A small-appliance manufacturer finds that the profit p (in dollars) generated by producing x microwave ovens per week is given by the formula p = 1 10 x(300 − x) provided that 0 ≤ x ≤ 200. how many ovens must be manufactured in a given week to generate a profit of $2134.40?

Answer 1

116 or 184 ovens must be manufactured in a given week to generate a profit of $2134.40

Explanation

Profit formula is:  $P=\frac{1}{10}x(300-x)$ , where $x$ is the number of microwave ovens produced per week.

As the manufacturer needs to generate a profit of $2134.40, that means we will plug $P= 2134.40$ into the above formula and then solve the equation for $x$

$2134.40=\frac{1}{10}x(300-x)\\\\ 21344=x(300-x)\\\\ 21344=300x-x^2\\\\ x^2-300x+21344=0\\\\ (x-116)(x-184)=0$

Using zero-product property, we will get....

$x-116 =0\\ \\ x= 116$

and

$x-184=0\\\\ x= 184$

So, 116 or 184 ovens must be manufactured in a given week to generate a profit of $2134.40