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.

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$