Question

The revenue function for a production by a theater group is R(t)= -50t^2+300t, where t is the ticket price in dollars. The cost function for the production is C(t)= 600-50t. Determine the ticket price that will allow the production to break even.

Answer 1

at break even, cost=revenue

-50t^2+300t=600-50t
divide by 60,combine terms, set to zero.

t^2-7t+12=0
(t-4)(t-3)=0
t=4 or t=3

I bet there is a profit between 3 and 4 dollars/ticket, and I suspect the maximum profit occurs at t=3.50

Answer 2

Thanks!