Question

the revenue for the school play is given by: r=-50t^2 + 300t, where “t” is ticket price in dollars. The cost to produce the play is given by: C=600-50t. Determine the ticket price that will allow Script & Cur to break even.

Answer 1

$3

Or

$4

Step-by-step explanation

The revenue function is

`r = - 50 {t}^(2) + 300t`

The cost function is,

C=600-50t

In order to break even, revenue must be equal to cost.

`600 - 50t= -50 {t}^(2) + 300t`

Group every term on the LHS.

`50 {t}^(2) - 300t - 50t + 600 = 0`

`50{t}^(2) - 350t + 600 = 0`

Divide through by 50.

`{t}^(2) - 7t + 12= 0`

Factor to obtain,

`(t - 3)(t - 4) = 0`

`t = 3 \: or \: t = 4`