Question

6. The revenue function for a production by a theatre group is

Answer 1

Answer:

When the ticket price is $3 or $4 the production will be in break even

Step-by-step explanation:

The correct question is

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

we know that

Break even is when the profit is equal to zero

That means

The cost is equal to the revenue

we have

$R(t)=-50t^2+300t$

$C(x)=600-50t$

Equate the cost and the revenue

$-50t^2+300t=600-50t$

solve for t

$-50t^2+300t+50t-600=0$

$-50t^2+350t-600=0$

Solve the quadratic equation by graphing

using a graphing tool

the solution is t=3 and t=4

see the attached figure

therefore

When the ticket price is $3 or $4 the production will be in break even