Answer:
2000 candy bars sold
$1200 in revenue
Step-by-step explanation:
Terms we need to know:
<u>Cost</u> "C": money needed/used to make the product (factory cost and candy bar expenses)
<u>Revenue</u> "R": money earned from selling the product (candy bars sold in a local store)
<u>Profit</u> "P": money left over after revenue is used to pay costs
<u>Break-even point</u> : 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
<u>Isolate "c"</u> 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.
