The dance company has a $10 cover charge, an average of 200 people will attend. For each $0.25 increase in admission price, the average number attending decreases by 1. What should the owner charge in order to make the most money? what is the maximum money that can be earned?

Question

The dance company has a $10 cover charge, an average of 200 people will attend.  For each $0.25 increase in admission price, the average number attending decreases by 1.  What should the owner charge in order to make the most money? what is the maximum money that can be earned?

Steve · Answer

If the price is 10.00 + .25x
attendance = 200 - x
money = attendance * price = (200-x)(10.00+.25x)
= -.25x^2 + 40x + 2000

this is a parabola with vertex at x = 40/.5 = 80

at x=80, admission is $30, money = 3600