Question

you invest in a new play. the cost includes an overhead of $40,000, 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) =
(type an expression using x as the variable.)

Explanation:

Step1: Analyze the cost components

The cost function \(C(x)\) has two parts: fixed overhead (\(40000\)) and variable production cost (\(2500x\)).

Step2: Formulate the cost function

Using the formula \(C(x)=\text{Fixed Cost}+\text{Variable Cost}\), we get \(C(x)=40000 + 2500x\).

Answer:

\(C(x)=40000+2500x\)