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Question 1066876: the owner of a 20-room motel must take $660 000 a year to cover costs and earn a reasonable profit.
a. if the average occupancy level is 70% and the same daily rate is charged for all occupied rooms, what should this rate be (to nearest dollar)?
b. if the owner decides to charge $30 more than the single occupancy rate if two or more people occupy the room, what should the two rates be (given that on average, two or more people are in 75% of the occupied rooms)? (answer in nearest doller)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! assume the rooms are available to rent 365 days in the year.
average cost per day is 660,000 / 365 = 1808.219178.
that's the average amount they need to collect each day throughout the year to cover expenses and make a profit.
20 rooms are available, but only 70% are occupied on average.
that means that 14 rooms per day are occupied on average throughout the year.
take 1808.219178 and divide it by 14 to get an average charge per room of 129.1585127.
round to the nearest dollar to get 129 per day.
that should be your answer to part a.
fyi,
129 per day doesn't cover 660,000.
round up to 130 per day and you'll be able to cover the 660,000 per day with a little to spare.
if the rooms are occupied by one person, then charge x dollars.
if the rooms are occupied by more than one person, then charge x + 30 dollars.
75% of the occupied rooms will have more than one occupant.
25% of the occupied rooms are therefore occupied by only one occupant.
you get:
.75 * 14 * (x + 30) + .25 * 14 * x = 1808.219178.
simplify to get .75 * 14 * x + .75 * 14 * 30 + .25 * 14 * x = 1808.219178
combine like terms to get 14 * x + 315 = 1808.219178
subtract 315 from both sides of the equation to get 14 * x = 1493.219178
solve for x to get x = 106.6585127.
the single occupancy rooms should charge 106.6585127.
the multiple occupancy rooms charge 30 dollars more than that.
the multiple occupancy rooms should charge 136.6585127.
round up in both cases and you get single = 107 and multiple = 137.
average total take in a day is .75 * 14 * 137 + .25 * 14 * 107 = 1813.
multiply by 365 and you get 661,745.
for part a, charge 129 per day if rounding to nearest dollar, or charge 130 per day if rounding up so you can cover the 660,000 required for the year.
for part b, charge 107 per day for single occupancy room and 137 per day for multiple occupancy room.
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