Question

you invest in a new play. the cost includes an overhead of $41,250, 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.
describe what this means.
a. the point where the cost and overhead cost are equal.
b. the point where revenue and production cost are equal.
c. the point where the cost and revenue are equal.
d. the point where revenue and overhead cost are equal

Explanation:

Step1: Write the cost function

The cost function \(C\) is the sum of the overhead cost and the production cost per performance times the number of performances.
\(C(x)=41250 + 2500x\)

Step2: Write the revenue function

The revenue function \(R\) is the revenue per performance times the number of performances.
\(R(x)=3125x\)

Step3: Determine the break - even point

Set \(C(x)=R(x)\):

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When \(x = 66\), \(R(66)=3125\times66 = 206250\) and \(C(66)=41250+2500\times66=41250 + 165000=206250\)

The break - even point is \((66,206250)\)

For the description of the break - even point:
The break - even point is the point where the cost and revenue are equal.

Answer:

a. \(C(x)=41250 + 2500x\)
b. \(R(x)=3125x\)
c. The break - even point is \((66,206250)\). C. The point where the cost and revenue are equal.