QuestionFind the cost function $C(x)$ for a theater with fixed costs of \$39000 and \$2400 per performance.

Studdy Solution

STEP 1

Assumptions1. The fixed overhead cost is \ $39000. The production cost per performance is \$24003.$ x $represents the number of sold-out performances4. The cost function$ C(x) $represents the total cost for$ x$ performances

STEP 2

The total cost for $x$ performances is the sum of the fixed overhead cost and the production cost for each performance.We can write this as $C(x) = Fixed\, overhead\, cost + (Production\, cost\, per\, performance \times Number\, of\, performances)$

STEP 3

Now, plug in the given values for the fixed overhead cost, production cost per performance, and the number of performances.
$C(x) = \$39000 + (\$2400 \times x)$

STEP 4

This is the cost function for the theater group.
$C(x) = \$39000 + \$2400x$ The cost function, $C(x)$ , where $C(x)$ represents the total cost for $x$ performances is $C(x) = \$39000 + \$2400x$ .

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