Question

In a town of 120,000 potential “football fans,” the football team draws the following attendees per game, at the various prices shown:

P	Q (in thousands)	Q (male) ((1’000s)	Q (female) (1’000s)	Revenue (1’000s)
0	120	60	60	0
10	90	50	40	900
20	60	40	20	1200
30	30	30	0	900

If the team can charge ANY prices it wants (including different prices to men and women), what price(s) should it charge to make the largest amount of revenue?

Answer 1

ANSWER:

when price is $10 the no of males watching will be 50,000 and the revenue from males will be 50,000 * $10 = $500,000 and the no of females watching will be 40,000 and the revenue from females will be 40,000 * $10 = $400,000

when price is $20 the no of males watching will be 40,000 and the revenue from males will be 40,000 * $20 = $800,000 and the no of females watching will be 20,000 and the revenue from females will be 20,000 * $20 = $400,000

when price is $30 the no of males watching will be 30,000 and the revenue from males will be 30,000 * $30 = $900,000 and the no of females watching will be 0 and the revenue from females will be 0 * $30 = $0

so the best combination is to charge $30 from males to earn $900,000 of revenue and charge $10 or $20 from females because their revenue will be $400,000 and so the maximum revenue will be $900,000 + $400,000 = $1,300,000

charge from males = $30

charge from females = $10 or $20

largest revenue = $1,300,000