Question

Candy bars are sold in a local store for 60 cents each. The factory has 1000 in fixed costs plus 10 cents additional expense for each bar made. Assuming all candy bars manufactured can be sold. Find the break-even point

Answer 1

Answer:

2000 candy bars sold

$1200 in revenue

Step-by-step explanation:

Terms we need to know:

Cost "C": money needed/used to make the product (factory cost and candy bar expenses)

Revenue "R": money earned from selling the product (candy bars sold in a local store)

Profit "P": money left over after revenue is used to pay costs

Break-even point : when there is no profit (the profit is 0), what is the total revenue and number of items sold?

Create equations for the question:

State your variables.

let 'c' be the number of candy bars sold

R(c) = 0.6c                    Candy bars sell for 60 cents each

C(c) = 0.1c + 1000          10 cents expense per candy bar and factory cost

P(c) = 0          When profit is 0, we are looking to break even

Profit = Revenue - Cost

P(c) = R(c) - C(c)             Substitute the expressions above

P(c) = 0.6c - (0.1c + 1000)

Simplify this equation first. Use the rule for subtracting binomials, where you change the positive/negative for each number inside the brackets.

P(c) = 0.6c - (0.1c + 1000)    Positive in brackets, negative when taken out

P(c) = 0.6c - 0.1c - 1000             Combine like terms

P(c) = 0.5c - 1000            General equation for this problem

0 = 0.5c - 1000                 Remember profit should be 0

Isolate "c" to find how many candy bars made will result in the break-even point.

0 + 1000 = 0.5c - 1000 + 1000        Add 1000 to both sides

1000 = 0.5c

1000/0.5 = 0.5c/0.5             Divide both sides by 0.5

2000 = c          Answer

c = 2000       Variable on left side for standard formatting

Now to find the revenue at the break-even point.

Go back to the revenue equation for this question. Substitute when "c" is 2000.

R(c) = 0.6c

R(2000) = 0.6(2000)        Multiply

R(2000) = 1200              Revenue at break even point

Therefore the break-even point is when 2000 candy bars are sold, which would provide $1200 in revenue.