Question

Break-Even Analysis: Popcorn

The business club is going to sell popcorn at hockey games. Since they are astute business men
and business women, they know that they will not make a profit right away because they have to
pay the cost of buying a popcorn machine. They need to know how many bags of popcorn they
must sell in order to cover the set-up costs. In other words, what is the break-even point for
their popcorn business?
The red and glass popcorn carts often seen at carnivals and fairs costs $450. This is the fixed
cost. Regardless of the number of bags of popcorn they make and sell, the machine cost will not
change.
1. The popcorn, butter, salt, and serving bags cost $15 for every 100 bags of popcorn. What is
the cost per bag for these consumables?
$15 per 100 bags = $.15 per bag
The variable cost changes depending on how many bags of popcorn they make. The more
popcorn they make, the more they spend on popcorn, butter, salt and bags. The variable cost is
$0.15 times the number of bags of popcorn.
The total cost is the variable cost plus the fixed cost.
Total Cost = Variable Cost+Fixed Cost
2. Write an equation for the Total Cost as a function of the number of bags of popcorn made.
Use the notation C(x) for total cost, and let x be the number of bags of popcorn they make.
((x) =115x+450
Each bag of popcorn sells for $1.00. The revenue is the amount of money they receive from
selling bags of popcorn. If they sell 20 bags of popcorn, they will receive $20, since each bag
sells for $1. The revenue they take in is the price per bag of popcorn multiplied by the number of
bags of popcorn sold.
(Price per Item) (Number of Items)
3. Write an equation for the Revenue as a function of the number of bags of popcorn sold. Label
the revenue function R(x).
Revenue =

Answer 1

Explanation:

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Answer 2

Answer: Price per Bag * Number of Bags = $1 * x = R(x)

To find the break-even point for the popcorn business, you need to find the number of bags of popcorn that need to be sold in order to cover the total cost, which includes the fixed cost of the machine and the variable cost of the consumables.

Calculate the cost per bag of popcorn for the consumables:

$15 for every 100 bags of popcorn ÷ 100 bags = $0.15 per bag.

Write an equation for the total cost as a function of the number of bags of popcorn made:

Total Cost = Variable Cost + Fixed Cost

Variable Cost = $0.15 * Number of Bags

Total Cost = $0.15 * Number of Bags + $450

Let C(x) represent the total cost where x is the number of bags of popcorn.

C(x) = $0.15 * x + $450

Write an equation for the revenue as a function of the number of bags of popcorn sold:

Revenue = Price per Bag * Number of Bags

Price per Bag = $1

Revenue = $1 * Number of Bags

Let R(x) represent the revenue where x is the number of bags of popcorn.

R(x) = $1 * x

Set the revenue equation equal to the total cost equation and solve for x, the number of bags of popcorn that need to be sold to reach the break-even point:

R(x) = C(x)

$1 * x = $0.15 * x + $450

$0.85 * x = $450

x = $450 ÷ $0.85 = 529 bags

Therefore, the business club needs to sell 529 bags of popcorn in order to reach the break-even point and cover their costs.

Explanation: