Problema Solution
The director of a play must decide how much to charge per ticket. If tickets cost c dollars each, a total of (75−5c) people will attend the play. Which ticket price will generate the most income?
Answer provided by our tutors
The income from total of (75−5c) people and cost of the ticket c is:
c(75 - 5c) = -5c^2 + 75c
The maximum of the parabolic function -5c^2 + 75c is reached for c = - b/2a, where a = - 5, b = 75, that is:
c = -75/(2*(-5))
c = $7.50
The ticket price of $7.50 will generate the most income.