Question

Meadow Inc. sells shoes for $135 each. The variable costs per shoe are $22 and the fixed costs per week are $5887. How many shoes must be sold to make a profit of $642.5 in a week?

Answer 1

Meadow Inc. needs to sell approximately 58 shoes to make a profit of $642.5 in a week. This calculation considers a selling price of $135 per shoe, variable costs of $22 per shoe, and fixed costs of $5887 per week.

Step-by-step explanation:

To calculate the number of shoes that must be sold to make a profit of $642.5 in a week, you can use the following formula:

`\[ \text{Profit} = (\text{Selling Price} - \text{Variable Cost}) * \text{Number of Shoes} - \text{Fixed Costs} \]`

Given:

Selling Price = $135

Variable Cost per shoe = $22

Fixed Costs = $5887

Desired Profit = $642.5

Now, let ( x ) be the number of shoes to be sold.

`\[ 642.5 = (135 - 22) * x - 5887 \]`

First, calculate the difference between the selling price and variable cost per shoe:

`\[ \text{Selling Price} - \text{Variable Cost} = 135 - 22 = 113 \]`

Now, the equation becomes:

`\[ 642.5 = 113x - 5887 \]`

Add ( 5887 ) to both sides of the equation:

`\[ 642.5 + 5887 = 113x \]`

`\[ 6529.5 = 113x \]`

Now, solve for ( x ):

`\[ x = (6529.5)/(113) \]`

`\[ x \approx 57.8761 \]`

Since you cannot sell a fraction of a shoe, you need to round up to the nearest whole number, as you can't sell a fraction of a shoe:

So, you would need to sell approximately 58 shoes to make a profit of $642.5 in a week.