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As part of their application for a loan to buy Lakeside Farm, a property they ho

ID: 2955588 • Letter: A

Question

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

a. Write the expression for total cost per month. Assume 30 days per month.
b. Write the expression for total revenue per month, first using the general variables, and second including the values of known variables).
c. If there are 12 guest rooms available, can they break even? What would be the profit with 12 rooms?
d. What percentage of rooms would need to be occupied, on average, to break even?

Explanation / Answer

a) total cost per month = 6000 + 20*30*n = 6000 + 600*n, where n is the number of guest rooms occupied b) total revenue = 75*30*n = 2250*n, where n is the number of guest rooms occupied c) Assuming all 12 rooms are occupied, we have: cost = 6000 + 600*12 = $13,200 revenue = 2250*12 = $27000 Yes - they most certainly can break even! d) To exactly break even: 6000+600*p*12 = 2250*p*12 => 6000 = 1650*p*12 => 500/1650 = p => p = 10/33 ~= 30.3%