contestada

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.

Respuesta :

kudzordzifrancis

ANSWER

$3

Or

$4

EXPLANATION

The revenue function is

[tex]r = - 50 {t}^{2} + 300t[/tex]

The cost function is,

C=600-50t

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

[tex]600 - 50t= -50 {t}^{2} + 300t[/tex]

Group every term on the LHS.

[tex]50 {t}^{2} - 300t - 50t + 600 = 0[/tex]

[tex]50{t}^{2} - 350t + 600 = 0[/tex]

Divide through by 50.

[tex]{t}^{2} - 7t + 12= 0[/tex]

Factor to obtain,

[tex](t - 3)(t - 4) = 0[/tex]

[tex]t = 3 \: or \: t = 4[/tex]