Question

The profit of a cell-phone manufacturer is found by the function Y= -2x^2 + 108x + 75, where x is the cost of the cell phone. At what price should the manufacturer sell the phone tomaximize its profits? What will the maximum profit be?

Answer 1

SOLUTION

From the equation

$y=-2x^2+108x+75$

At maximum price, the derivative of the equation will be equal to zero, so we have

$\begin{gathered} y=-2x^2+108x+75 \\ y^{\prime}=-4x+108+0 \\ y^{\prime}=-4x+108=0 \\ -4x+108=0 \\ 4x=108 \\ \text{dividing both sides by 4, we have } \\ x=\frac{108}{4} \\ x=27 \end{gathered}$

Hence the answer is 27