Simon owns a small car wash and detailing center. He charges $12 per wash. He pays each of his two employees $12 per hour. The employees each work 40 hours per week. Simon's other costs amount to $450 per week. Simon wants to earn an average profit of at least $3.25 per wash each week. How many car washes could the staff give in a week so that Simon will earn an average of at least $3.25 over wash?
Income/wk. = $12/wash * XWASHES = $12X.
Cost/wk. = ($12/h*40h)2 + $450/wk. = $1410.
Profit/wk. = 12x - 1410 = $3.25/wash * xwashes. = $3.25x.
Profit/wk. = 12x - 1410 = 3.25x, X = 161.14 or 162 Washes.
To determine the number of car washes Simon's staff should give in a week to earn an average profit of at least $3.25 per wash, we need to calculate Simon's total costs and then determine the minimum number of car washes needed to achieve the desired profit.
First, let's calculate Simon's total labor costs:
Labor cost per employee per week = 2 employees * $12 per hour * 40 hours per week = $960 per employee per week
Total labor cost per week = 2 employees * $960 per employee per week = $1,920 per week
Next, let's calculate Simon's total costs:
Total costs per week = Labor costs per week + Other costs per week = $1,920 + $450 = $2,370 per week
To calculate the minimum number of car washes needed, use the following formula:
Minimum number of car washes = (Total costs per week / (Car wash price - Average profit per wash))
Plugging in the values, we get:
Minimum number of car washes = ($2,370 / ($12 - $3.25))
Calculating further:
Minimum number of car washes = ($2,370 / $8.75)
Minimum number of car washes = 270.86 (rounded up to 271)
Therefore, Simon's staff needs to give at least 271 car washes in a week to earn an average profit of at least $3.25 per wash.