Question

The cost of manufacturing halogen lights includes $1,250 per day to pay for overhead costs, and $12 per day for labor and materials. The halogen lights sell for $12 each. What is the fewest number of halogen lights the company must sell in one day to break even?

Answer 1

Hey there!

To solve this problem, you need to calculate how many halogen lights need to be sold in one day. For one day, the overhead and labor/materials costs will remain constant, meaning that they won't have a variable attached to them. The only variable needed is for the number of halogen lights, which can be represented by x. 

First, you will add the total daily costs together. Then, you need to set that total equal to the amount of halogen lights sold at $12 each. This gives you:

1250 + 12 = 12x

Now, you can solve for x:

1250 + 12 = 12x (simplify)
1262 = 12x (divide both sides by 12)
105.167 = x (round up, since you can't sell parts)
106 (total amount of halogen lights sold per day to break even)

You can check this by plugging 106 back into your equation:

1262 = 12x
1262 = 12(106)
1262 = 1272 (goes slightly over since 105 lights wouldn't make enough)

Your answer will be 106 lights.

Hope this helped you out! :-)