Question

An organizer for a party has determined her costs to be $697 plus $13 per attendee. If each participant is paying $35, how many people are needed for the party to break even? Round your answer to the nearest person.

Answer 1

32 people

Explanation:

The general equation for the cost function is:

C(q) = mq + c, where

• mq is the marginal cost (increase in cost per 1 additional item produced),
• and c is the fixed costs (an individual or business pays this amount even when no items are produced).

For the organizer, the fixed cost is $697, and the marginal cost 13.

The general equation for the revenue function is:

R(q) = pq, where

• p is the marginal price (increase in price of an item per 1 additional item sold),
• and q is the quantity.

For the organizer, the marginal price is $35.

The break-even point is the point at which revenue equals cost. Thus, we can determine how many people are needed to break even by setting C(q) equal to R(q) and solving for q:

C(q) = R(q)

697 + 13q = 35q

697 = 22q

31.68181818 = q

32 = q

Thus, about 32 people are needed for the party to break-even.