Question

The revenue for a production by a theatre group is y = -4t^2 + 30t, where t is the ticket price in dollars. The cost for the production is y = 30 - 5t. Determine the ticket price that will allow the production to break even.

a) $3.75
b) $4.00
c) $4.50
d) $5.00

Answer 1

The ticket price that will allow the production to break even is $6.

Step-by-step explanation:

To determine the ticket price that will allow the production to break even, we need to set the revenue equal to the cost and solve for t.

The revenue for the production is given by y = -4t^2 + 30t

The cost for the production is given by y = 30 - 5t

Setting the revenue equal to the cost:

-4t^2 + 30t = 30 - 5t

Combining like terms:

-4t^2 + 35t = 30

Bringing all terms to one side:

-4t^2 + 35t - 30 = 0

Factoring:

(-4t + 5)(t - 6) = 0

Setting each factor equal to zero:

-4t + 5 = 0
t = 5/4

t - 6 = 0
t = 6

Since ticket prices cannot be negative, the ticket price that will allow the production to break even is $6.