Quadratics Optimisation Question

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? Which ticket price gives this maximum revenue?

Answer 1

1200 at $20

1140 at $22

0 at $40

600 at $0

slope = -2/60= -1/30= change in price over change in quantity purchased

y= -(1/30)(x-1200) +20

y=-x/30 +60

intercepts are (0, 60) and (1800,0)

midpoint (900, 30) with $30 price gives maximum revenue =900x30 = $27,000