What was the maximum revenue from the apartments?

Question

the number of apartments that can be rented in a 100-unit apartment complex decreases by one for each increase of $25 in rent. The revenue generated from rent after x increases of $25 is given by the equation R(X)=-25x^2+1700x+80,000.

Answer 1

The vertex of a quadratic in the form  ax² + bx + c  occurs where x = -b/(2a).  Here b = 1700 and a = -25 so the vertex is located at  

 

x = -1700(2*(-25)) = 1700/50 = 34  

 

To find the revenue plug x = 34 into the equation  

 

R(34) = -25(34²) + 1700(34) + 80000

         = -25*1156 + 57800 + 80000

         = -28900 + 137800

         = $108900  

 

Since a = -25 is negative the quadratic opens downward which means that the vertex denotes the maximum value