Answer
See below.
Work Step by Step
Let $x$ be each $ \$10 $ decrease in price. The revenue can be modeled by the function: $R(x)=(140-10x)(50+5x)=7000+200x-50x^2$.
Let's compare $R(x)$ to $f(x)=ax^2+bx+c$. We can see that a=-50, b=200, c=7000. $a\lt0$, hence the graph opens down, and its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{200}{2\cdot(-50)}=2.$ Hence the maximum value is $R(2)=-50(2)^2+200(2)+7000=7200.$
Thus they should charge $120$.
