A shoe store costs $1800 dollars a month to operate. The average wholesale cost of each pair of shoes is $25, and the average price of each pair of shoes is $65. How many pairs of shoes must the store sell each month to break even?
break-even means that cost = revenue
So, if there are x pairs of shoes, you need
1800 + 25x = 65x
To determine the number of pairs of shoes the store must sell each month to break even, we need to consider the costs and revenue involved.
First, let's calculate the store's fixed costs per pair of shoes:
Fixed costs per pair of shoes = Total monthly operating costs / Number of pairs of shoes
Given that the fixed monthly operating costs are $1800, and the average wholesale cost of each pair of shoes is $25:
Fixed costs per pair of shoes = $1800 / $25
Fixed costs per pair of shoes = 72 pairs of shoes
Next, let's calculate the profit per pair of shoes:
Profit per pair of shoes = Selling price per pair of shoes - Wholesale cost per pair of shoes
Given that the average price of each pair of shoes is $65 and the average wholesale cost is $25:
Profit per pair of shoes = $65 - $25
Profit per pair of shoes = $40
Finally, we can calculate the break-even point by dividing the fixed costs per pair of shoes by the profit per pair of shoes:
Break-even point = Fixed costs per pair of shoes / Profit per pair of shoes
Break-even point = 72 pairs of shoes / $40
Break-even point = 1.8 pairs of shoes
Since it is not possible to sell a fractional part of a shoe, the store would need to sell at least 2 pairs of shoes each month to break even.