116 or 184 ovens must be manufactured in a given week to generate a profit of $2134.40
Explanation
Profit formula is: [tex] P=\frac{1}{10}x(300-x) [/tex] , where [tex] x [/tex] 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 [tex] P= 2134.40 [/tex] into the above formula and then solve the equation for [tex] x [/tex]
[tex] 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 [/tex]
Using zero-product property, we will get....
[tex] x-116 =0\\ \\ x= 116 [/tex]
and
[tex] x-184=0\\\\ x= 184 [/tex]
So, 116 or 184 ovens must be manufactured in a given week to generate a profit of $2134.40
