A retailer who sells backpacks estimates that by selling them for x dollars each, she will be able to sell 100−x backpacks each month. The quadratic function R(x)=−x2+100x is used to find the revenue, R, received when the selling price of a backpack is x. Find the selling price that will give her the maximum revenue, and then find the amount of the maximum revenue.

Accepted Solution

Answer:x = 50R = $2500Step-by-step explanation:Given in the question a quadratic equation,−x² + 100xTo find the selling price, x, which will give highest revenue, y, we will find maximum value of parabola curve −x² + 100xThe value of -b/2a tells you the value x of the vertex of the function −x² + 100xhere a = -1         b = 100Selling price = -(100)/2(-1)                     =   50  R = −(50)² + 100(50)   = 2500