Answer:
3.75x = 450 + 1.50x
They should sell 200 bags of popcorn to break even
Step-by-step explanation:
Business Modeling
When modeling the operation of a business, there are some magnitudes that should be managed to properly control the profits of the business. Those magnitudes are Costs, Revenue, and Profits.
The profit is the difference between the costs and the revenue as follows:
P(x) = R(x) - C(x)
Where x is the number of units produced and sold.
The break-even level is the value of x that produces zero profits, i.e.,
R(x) = C(x)
The costs associated to sell popcorn consist of a fixed amount of $450 plus a variable cost of $1.50 for every popcorn. Thus the total cost function is:
C(x) = 450 + 1.50x
The income or revenue is the selling price times the number of popcorns:
R(x) = 3.75x
The break-even level can be calculated by solving the equation:
3.75x = 450 + 1.50x
Solving the equation:
3.75x - 1.50x = 450
2.25x = 450
x = 450/2.25
x = 200
They should sell 200 bags of popcorn to break even
