Question

A factory sells backpacks for $40.00 each. The cost to make 1 backpack is $10.00. In addition to the cost of making backpacks, the factory has operating expenses of $12,000 per week. The factory's goal is to make a profit of at least $9,800 per week. Which inequality represents the number of backpacks, x, that need to be sold each week for the factory to meet this goal?

Answer 1

The factory needs to sell 327 packbacks to make at least 9,800 per week.

Explanation:

We know that each backpacks is sold for $40.00.

The goal is to make at least $9,800 per week. With this information we can define the inequality

`40x -10x \leq 9,800`

Where
`x` represents backpacks. Notice that this inequality is about profits, that's why we subtract the cost from the sell price, in this case, the profid margin is $30.00 per backpack, so

`30x\leq 9,800`

Solving for
`x`

`x\leq (9800)/(30)\\ x \leq 326.67`

Therefore, the factory needs to sell 327 packbacks to make at least 9,800 per week.