Question

Please help me with this word problem!!!

Carlita plans to establish a second restaurant, open five days a week, 50 weeks a year. Here are her costs:
• Rent: $7,200/month
• The average customer pays $45.47
• Carlita’s average food cost per customer: $20.18
• Insurance: $4,200/year
• Carlita hires 2 servers for 8 hours/day and a part-time helper for 4 hours/day.

She pays $15 per hour and pays employer Social Security tax (6.2% of gross pay) and Medicare tax (1.45% of gross pay).

How many customers would Carlita need to serve each year for the restaurant to break even? Round to the nearest whole number.

Hint: “Break even” means sales and expenses are equal and the owner neither makes nor loses money.

Answer 1

The number of customers needed to break even is

`\simeq 6775.`

Explanation:

Rent per month = $ 7200

Rent per year, $
`7200 * 12`

= $ 86400 -------------(1)

Insurance per year = $ 4200 ---------(2)

Total direct cost for 2 servers (withoout tax) per year,

= $
`2 * 15 * 8 * 5 * 50`

= $ 60000

Total cost for helper ( without tax) per year,

= $
`4 * 15 * 5 * \50`

= $ 15000

Total cost for employees per year (without tax),

= $ (60000 +15000) = $ 75000

Total cost per year for employees including tax,

$
`\frac {(75000 * (100 + 6.2 + 1.45)}{100}`

= $
`\frac {(75000 * 107.65 }{100}`

= $ 80737.5 -----------------------(3)

So,

total cost for running the restaurant (except food)

= (1) + (2) + (3) = $
`(86400 + 4200 + 80737.5)`

= $ 171337.5

Average total profit per customer,

= ( Average per customer payment - average cost of food per customer)

= $ (45.47 - 20.18)

= $ 25.29

So, total number of customer needed to break even,

=
`\frac {171337.5}{25.29}`

\simeq 6775