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

Step-by-step explanation

Profit formula is:
`P=(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=(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