Question

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

Answer 1

Answer:

2000 bars, or $1200

Explanation:

Let x represent the number of candy bars that are sold.  Since they are sold for $0.60 each, this gives us the expression

0.60x

to represent the profit.

The factor has $0.10 per candy bar additional expense; this gives us the expression

0.10x.

However the factory also has $1000 fixed costs; this gives us

0.10x + 1000

to represent the costs.

The break-even point is the point where these two expressions are equal; this gives us the equation

0.60x = 0.10x + 1000

Subtract 0.10x from each side:

0.60x - 0.10x = 0.10x + 1000 - 0.10x

0.50x = 1000

Divide both sides by 0.50:

0.50x/0.50 = 1000/0.50

x = 2000

The break-even point is 2000 candy bars, which would sell for

0.60(2000) = $1200

Answer 2

Let the number of candybars made be x. We first need to find an equation for revenue, which is profit - cost.

Lets work out what profit is first. Each candybar sells for 60 cents, therefore 0.60x represents how much profit is made from the candybars.

Next, lets work out cost. We know there's a fixed cost of 1000 plus the cost per bar which is 0.10x. So the equation for cost is 1000 + 0.10x.

Finally, lets solve for revenue.

R = 0.60x - (1000 + 0.10x)

R = 0.60x - 1000 - 0.10x

R = 0.50x - 1000

So, this is our revenue equation. To break even means that revenue is 0. The company isn't making or losing any money. Therefore, we can set this equation to 0 to find how many bars need to be made to break even.

0 = 0.50x - 1000

1000 = 0.50x

2000 = x

Thus, the company needs to make 2000 candy bars to break even.