A hotel sells its single room nights for an average of $100 and its double room nights for an average of $130. The variable cost per single room night sold is $10 and the variable cost per double room night sold is $12. The hotel has annual fixed costs of $1,358,000. In the past the hotel has sold three single rooms for each double room sold. Based on the 3:1 sales mix achieved in the past, what combination of single and double room sales must be made in order for the hotel to breakeven?

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Quizplus · Accepted Answer

To calculate the break-even point, we first determine the contribution margin per unit for both single and double rooms. For single rooms, the contribution margin is $100 - $10 = $90. For double rooms, it's $130 - $12 = $118. Given the 3:1 sales mix, for every 4 rooms sold, 3 are single and 1 is double. The weighted average contribution margin per room is then $\frac{(3 \times 90) + (1 \times 118)}{4} = \frac{388}{4} = 97$. To cover the fixed costs of $1,358,000, the number of rooms (N) needed is $N = \frac{1,358,000}{97} \approx 14,000$ rooms in total. Given the 3:1 mix, this translates to 10,500 singles (3/4 of 14,000) and 3,500 doubles (1/4 of 14,000).

A Hotel Sells Its Single Room Nights for an Average