Quadratic Function

Question

The soccer club sells hoodies as a fund-raiser. They sell 1200 shirts a year at $20 each. They are planning to increase the price. A survey indicates that, for every $2 increase in price, there will be a drop of 60 sales a year. What is the maximum revenue the club could make?

Answer 1

We can let x represent the number of $2 price increases.

The new price will be:

20 + 2x

The number of hoodies sold will be:

1200 - 60x

Revenue is price times quantity, so:

R(x) = (20 + 2x)(1200 - 60x)

= -120x² + 1200x + 24000

Since this quadratic opens downward, its vertex gives the minimum revenue.

Use the vertex formula:

x = -b / 2a

x = -1200 / 2(-120)

x = 5

So, the price should be increased 5 times by $2:

20 + 2(5) = $30

The number of hoodies sold would be:

1200 - 60(5) = 900

Therefore, the maximum revenue is:

30(900) = $27000

So, the club could make a maximum revenue of $27,000 per year.

Answer 2

1200p

p(1200-(60*i/2))

price

increase