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A restaurant averages ales of $120,000 when serving 20,000 guests. The restaurant's variable costs when 20,000 is $90,000. The contribution margin per guest is $1.50. Fixed monthly costs are $50,000. What is the restaurant's monthly breakeven point in sales dollars?

Respuesta :

Answer: Restaurant's monthly breakeven point in sales is $31333.

Step-by-step explanation:

Since we have given that

Number of guests = 20,000

Average sales = $120,000

Contribution margin per guest = $1.50

Let the number of sales be 'x'.

Cost per sales would be

[tex]\dfrac{120000}{20000}\\\\=\$6[/tex]

Margin contributed by 2000 guests would be

[tex]1.50\times 20000\\\\=\$3000[/tex]

So, Revenue function would be

[tex]6x+3000[/tex]

Fixed monthly cost = $ 50,000

Variable cost for 20000 guests = $90000

So, Variable cost per sale would be

[tex]\dfrac{90000}{20000}\\\\=\$4.5[/tex]

So, Cost function would be

[tex]4.5x+50000[/tex]

Breakeven point would be

Cost function = Revenue function

[tex]6x+3000=4.5x+50000\\\\6x-4.5x=50000-3000\\\\1.5x=47000\\\\x=\dfrac{47000}{1.5}\\\\x=\$31333.33\\\\x=\$31333[/tex]

Hence, Restaurant's monthly breakeven point in sales is $31333.

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