Question

The profit, P dollars, earned by a saleswoman selling scented candles is approximated to be P=-10x^2+300x-250, where x dollars is the selling price of one scented candle. What selling price gives the maximum profit?

$10
$30
$15
$7.50

Answer 1

the selling price that gives the maximum profit is $15

Explanation:

The profit, P dollars, earned by a saleswoman selling scented candles is approximated to be P=-10x^2+300x-250

This is a quadratic equation and the graph of P against x will give a parabola with a vertex whose value will be the maximum price

The maximum price occurs at x =

-b/2a

From the equation,

a = -10

b = 300

c = - 250

-b/2a = -300/2×-10= -300/-20

= 15

This gives the vertex of the parabola

Therefore, the selling price that gives the maximum profit is $15