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statuscvo [17]
3 years ago
6

A restaurant averages ales of $120,000 when serving 20,000 guests. The restaurant's variable costs when 20,000 is $90,000. The c

ontribution margin per guest is $1.50. Fixed monthly costs are $50,000. What is the restaurant's monthly breakeven point in sales dollars?
Mathematics
1 answer:
Katarina [22]3 years ago
3 0

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

Margin contributed by 2000 guests would be

1.50\times 20000\\\\=\$3000

So, Revenue function would be

6x+3000

Fixed monthly cost = $ 50,000

Variable cost for 20000 guests = $90000

So, Variable cost per sale would be

\dfrac{90000}{20000}\\\\=\$4.5

So, Cost function would be

4.5x+50000

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

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

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If you divide one of the roots of the equation 4x2+bx−27=0 by the other root, the quotient will be −3. Find b.
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  ±12   (two answers)

<h3>Explanation:</h3>

Suppose one root is <em>a</em>. Then the other root will be -3<em>a</em>. The product of the two roots is the ratio of the constant coefficient to the leading coefficient:

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Then the other root is

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  b = ±12

_____

<em>Check</em>

For b = 12, the equation factors as ...

  4x² +12x -27 = (2x -3)(2x +9) = 0

  It has roots -9/2 and +3/2, the ratio of which is -3.

For b = -12, the equation factors as ...

  4x² -12x -27 = (2x +3)(2x -9) = 0

  It has roots 9/2 and -3/2, the ratio of which is -3.

4 0
3 years ago
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