Finding The Maximum Using The Vertex Worksheet With Answer Key (Page 2 of 5) in pdf

Finding The Maximum Using The Vertex Worksheet With Answer Key Page 2

Graph of the equation: A = -x

+ 80x

1800

1600

1400

1200

1000

800

600

400

200

100

Example2:

A sporting goods store sells basketball shorts for $8. At this price their weekly sales are

approximately 100 items. Research says that for every $2 increase in price, the manager can

expect the store to sell five fewer pairs of shorts. Determine the maximum revenue the

manager can expect based on these estimates. What selling price will give that maximum

revenue, and how many shorts will be sold?

Let x = # of $2 price increases

Let R = the revenue

Based on no changes, the revenue would have been R = (price)(shorts_sold) = (8)(100).

With the expected changes:

The new price = 8 + 2x

{for every increase, price goes up by $2}

The shorts sold = 100 – 5x

{for every increase, number of shorts sold goes down by 5}

Formula:

R = (8 +2x)(100 – 5x)

To get the maximum revenue, rewrite the above as a quadratic function and find the vertex

(maximum values).

Finding The Maximum Using The Vertex Worksheet With Answer Key Page 2