Question

The revenue function for a production by a theatre 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

Break even is the value of t where revenue=cost or R(t)=C(t)

set equal each other

-50t^2+300t=600-50t
multiply both sides by -1
50t^2-300t=50t-600
divide both sides by 50
t^2-6t=t-12
minus t-12 from both sides
t^2-7t+12=0
factor
(t-4)(t-3)=0
set each to zero
t-4=0
t=4

t-3=0
t=3
the cost is $3 or $4

it will first break even at t=3$

Answer 2

The break even exists when the cost of the process is equal to the revenue of the selling. In this case, -50t^2 + 300t  = 600-50t; 50t^2 -350 t  + 600 = 0. t is the number of tickets. In this problem, the breakeven point is at t equal to 4 and 3 tickets. the ticket price should be 600- 50*3 equal to 450 dollars as this is the greater one between the two to gain more revenue after break even