Question

Decision

As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected:

Monthly fixed cost (loan payment, taxes, insurance, maintenance)	$6000
Variable cost per occupied room per night	20
Revenue per occupied room per night	75

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a.	Write the expression for total cost per month. Assume 30 days per month.
b.	Write the expression for total revenue per month.
c. ​	If there are 12 guest rooms available, can they break even? What percentage of rooms would need to be occupied, on average, to break even?

variables in a production process are those that cannot be controlled by the manager

Answer 1

The answer to Q a:

To derive the expression, first identify the fixed cost and the variable cost. The expression is Y = aX+ b. Here, b is fixed cost, i.e. 6000 and ‘a’ is a variable cost, i.e. 20*30. As the variable cost per occupied room is 20 per night, to get the monthly cost, it is multiplied by 30. Here, X is the number of rooms occupied.

Y(x) = 6000 + 20(30) X (monthly)

The answer to Q b:

Revenue per occupied room per night is 75, so the revenue expression will be as follows.

R(x) = 75(30) X (monthly)

The answer to Q c:

Fixed cost = 6000

Variable cost per room per night = 20

Revenue per room per night = 75

Breakeven point = Fixed cost / (revenue per room per night – Variable cost per room per night) *30= 6000 / (75 – 20) * 30 = 6000 / 55 * 30 = 6000 / 1650 = 3.64 = 4 rooms per night. The hotel has enough rooms to break even.

Occupancy rate = (Break-Even point / total rooms)*100 = (4/12) *100 = 100/3 = 33.33 %

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