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You invest in a new play. The cost includes an overhead of ​$ 36 comma 250 36,250​, plus production costs of​ $2500 per performance. A​ sold-out performance brings in​ $3125. (In solving this​ exercise, let x represent the number of​ sold-out performances.) a. Write the cost​ function, C. b. Write the revenue​ function, R. c. Determine the​ break-even point. Describe what this means. a. Write the cost​ function, C. ​C(x) equals = nothing ​(Type an expression using x as the​ variable.)

Respuesta :

Answer:

(a). [tex]C(x)=36,250+2500x[/tex]

(b). [tex]R(x)=3125x[/tex]

(c). Break-even point = 58 sold-out performances.

Step-by-step explanation:

Let x represent the number of​ sold-out performances.

(a). We have been given that the cost of a new play includes an overhead of ​$36,250​, plus production costs of​ $2500 per performance.

So the cost of investing in x performances, C(x), will be: [tex]C(x)=36,250+2500x[/tex]

(b). We are also told that a sold-out performance brings in​ $3125.

So the revenue collected from x performances, R(x),will be: [tex]R(x)=3125x[/tex]

(c). Since we know that break-even is the point, where total costs (expenses) and total sales (revenue) are equal. At this point profit equals 0.

To find the break even point, let us equate our cost and revenue functions as:

[tex]36,250+2500x=3125x[/tex]

[tex]36,250+2500x-2500x=3125x-2500x[/tex]

[tex]36,250=625x[/tex]

[tex]x=\frac{36,250}{625}[/tex]

[tex]x=58[/tex]

Therefore, the break-even point is 58 sold-out performances.