Question

Mary's children decide to run a lemonade stand to earn some extra money. The cost to start the buisness is $1.20 and each cup of lemonade costs 6 cents to make. If lemonade sells for 10 cents a cup, how many cups must Mary's children sell to make a profit?

Answer 1

The correct answer is more than 30 cups.

Explanation:

Step 1:

Determine the cost function for this business.

The fixed costs for this business is $1.20. The variable costs for this business is
`0.06x` where
`x` is the number of cups of lemonade created.

The cost function
`C(x)` for this business is the sum of the fixed costs and the variable costs. For this businesses the cost function is,

`C(x)=1.20+0.06x`

Step 2;

The next step is to determine the revenue function for this business.

Since every unit sells for $0.10, the revenue function
`R(x)` for this business is,

`R(x)=0.1x.`

Step 3

The next step is to realize that the business will make a profit after it's break even point, i.e the point at which the revenue from the business is equal t the cost of operating the business. The break even point is calculated as show blow,

`R(x)=C(x)\\\implies 0.10x=1.20+0.06x\\\implies 0.10x-0.06x=1.2\\\implies 0.04x=1.20\\\implies x=(1.20)/(0.04) =30`

The break even point occurs at 30 cups of lemonade sold. To makes a profit, the stall has to sell more than 30 cups.