Question

Sue makes and sells cupcakes. If she has a cost of $1,500 per year plus a cost of $1 per cupcake, how many cupcakes must she sell in order to make a profit if each cupcake sells for $3?

Answer 1

Sue must sell over 750 cupcakes to make a profit. The break-even point is calculated by dividing the fixed costs by the profit per cupcake, which after calculation is found to be 750 cupcakes.

Step-by-step explanation:

To determine how many cupcakes Sue must sell to make a profit, we need to calculate the break-even point, and then find any number of cupcakes sold beyond that point. Since the selling price is $3 per cupcake, and the cost is $1 per cupcake, Sue has a profit of $2 for each cupcake sold after covering the variable cost. In addition to this variable cost, she also has a fixed cost of $1,500 per year.

To calculate the break-even point (BEP), we use the formula: BEP = Fixed Costs / (Selling Price per Unit - Variable Cost per Unit), which translates to BEP = $1,500 / ($3 - $1) = $1,500 / $2 = 750 cupcakes. Therefore, Sue needs to sell more than 750 cupcakes to start making a profit.

Answer 2

751 cupcakes must be sold to make a profit

Step-by-step explanation:

From the question we are told that

Annual cost= $1,500 per year plus a cost of $1 per cupcake

Each cup cake sell at $3

Generally the profit off the top of each cupcake is $2

Therefore

`(1500)/(2)=750`

This implies that 750 cupcakes will be sold to cover the annual cost excluding cupcake cost

Generally

751 cupcakes=$1502

Total Annual cost to make a profit

`1(cost\ of\ each\ cupcake)*751+1500=\$2251`

Total Annual sale

`3(sale of each cupcake)*751=\$2253`

Mathematically

`2253\$-2251\$=2\$`

Therefore

751 cupcakes must be sold to make a profit