Respuesta :
If Mr. Stern charges a monthly rent of $200, we still can rent all suites. An average increase of $5 in the monthly rent imply in the addition of one suite vacant.
Therefore, the total monthly revenue r in function of the number of vacant units v can be writen in the form:
[tex]\begin{gathered} r=(200+5v)\cdot(60-v) \\ r=-5v^2+100v+1200 \\ 0\leq v\leq60 \end{gathered}[/tex]The monthly rent m is given by:
[tex]m=200+5v[/tex]The value of v that maximize the total revenue r is the one found in the vertex of the parabola that represents r:
[tex]v_{\max }=-\frac{100}{2\cdot(-5)}=10[/tex]Therefore, the monthly rent that maximize the total revenue is m = 200 + 5*10 = $700
The monthly revenue with this monthly rent is:
[tex]r=-5\cdot10^2+100\cdot10+1200=\text{ \$1700}[/tex]
