SOLUTION: Steve invests in a circus production. The coast includes an overhead of $81,000, plus production costs of $7,000 per performance. A sold-out performance brings in $16,000, Determin

Question 425882: Steve invests in a circus production. The coast includes an overhead of $81,000, plus production costs of $7,000 per performance. A sold-out performance brings in $16,000, Determine the number of sold-out performances, x, needed to break even.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
c = f + i*x
c = cost
f = fixed cost
i = incremental cost
x = number of increments

f = 81,000 fixed overhead
i = 7,000 per performance
x = number of performances

r = 16,000 per performance
x = number of performances

formula to break even is:

r*x = f + i*x

this becomes:

16,000*x = 81,000 + 7,000*x

subtract 7,000 * x from both sides of the equation to get:
16,000*x - 7,000*x = 81,000
combine like terms to get:
9,000*x = 81,000
divide both sides of equation by 9,000 to get:
x = 9

if we did this correctly, steve should break after 9 performances.

after 9 performances, revenue = 9 * $16,000 = $144,000

after 9 performances, cost = $81,000 + 9 * $7,000 = $81,000 + $63,000 = $144,000

that's the break even point.

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