Question

Tom wants to open a store that sells hats. He thinks he can sell them for $20 each. He estimates his monthly expenses to be $3000, and it will cost him $8 for each hat. Tom wants to analyze his estimated revenues and expenses to see how many hats he would need to sell each month in order to break even. He uses x to represent the number of hats and y to represent the total dollars. If Tom sells 250 hats, he will break even. How many hats does Tom need to sell each month to make a profit of $1,200?

Answer 1

We have to model the profit for his business.

The fixed cost is $3000.

The variable cost is $8 per hat and the price is $20 per hat.

Let x be the number of hats sold, then we can model the profit y as:

`\begin{gathered} y=20x-8x-3000 \\ y=12x-3000 \end{gathered}`

We have to calculate the number of hats x for a profit y = 1200.

We can do it as:

`\begin{gathered} y=1200 \\ 12x-3000=1200 \\ 12x=1200+3000 \\ 12x=4200 \\ x=(4200)/(12) \\ x=350 \end{gathered}`

Answer: to make a profit of $1200 he needs to sell 350 hats.