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
![\dfrac{120000}{20000}\\\\=\$6](https://tex.z-dn.net/?f=%5Cdfrac%7B120000%7D%7B20000%7D%5C%5C%5C%5C%3D%5C%246)
Margin contributed by 2000 guests would be
![1.50\times 20000\\\\=\$3000](https://tex.z-dn.net/?f=1.50%5Ctimes%2020000%5C%5C%5C%5C%3D%5C%243000)
So, Revenue function would be
![6x+3000](https://tex.z-dn.net/?f=6x%2B3000)
Fixed monthly cost = $ 50,000
Variable cost for 20000 guests = $90000
So, Variable cost per sale would be
![\dfrac{90000}{20000}\\\\=\$4.5](https://tex.z-dn.net/?f=%5Cdfrac%7B90000%7D%7B20000%7D%5C%5C%5C%5C%3D%5C%244.5)
So, Cost function would be
![4.5x+50000](https://tex.z-dn.net/?f=4.5x%2B50000)
Breakeven point would be
Cost function = Revenue function
![6x+3000=4.5x+50000\\\\6x-4.5x=50000-3000\\\\1.5x=47000\\\\x=\dfrac{47000}{1.5}\\\\x=\$31333.33\\\\x=\$31333](https://tex.z-dn.net/?f=6x%2B3000%3D4.5x%2B50000%5C%5C%5C%5C6x-4.5x%3D50000-3000%5C%5C%5C%5C1.5x%3D47000%5C%5C%5C%5Cx%3D%5Cdfrac%7B47000%7D%7B1.5%7D%5C%5C%5C%5Cx%3D%5C%2431333.33%5C%5C%5C%5Cx%3D%5C%2431333)
Hence, Restaurant's monthly breakeven point in sales is $31333.