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
[tex]R(t)=-50t^2+300t[/tex]
[tex]C(x)=600-50t[/tex]
Equate the cost and the revenue
[tex]-50t^2+300t=600-50t[/tex]
solve for t
[tex]-50t^2+300t+50t-600=0[/tex]
[tex]-50t^2+350t-600=0[/tex]
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
