Shannon G.

asked • 07/22/22

please help not sure how to calculate

Suppose Cineplex at Masonville Place can sell out a 300-seat theatre when tickets are sold for $24. For each $3 increase, 15 less tickets will be sold. Use a quadratic relation to determine the necessary ticket price to earn maximum revenue. 

Peter R.

tutor
It's 15 FEWER tickets, not less. The no. of tickets is a discrete value (countable). Ex: You say less sugar, not fewer sugar, because the measurement of sugar is continuous (it's never exactly a pound or a tablespoon). You measure sugar, you don't count it (except for sugar in cubes!).
Report

07/24/22

1 Expert Answer

By:

Yefim S. answered • 07/22/22

Tutor
5 (20)

Math Tutor with Experience

See tutors like this
See tutors like this

Let x dollars is necessary price. Then (x - 24)/3 is so many times increasing price. Now number of sold tickets

is (300 - (x - 24)/3·15) = (300 - 5x + 120) = 420 - 5x, and revenue R(x) = (420 - 5x)x = 420x - 5x2 =

-5(x2 - 84x + 1764) + 8820 = 8820 - 5(x - 42)2.

Now we see that when price is $42 per ticket we have maximum revenue $8820

Upvote • 0 Downvote
More
Report

Shannon G.

thank you !
Report

07/22/22

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.