Question

Tim Urban, Owner/Manager Of Urban's Motor Court In Key West, Is Considering Outsourcing The Daily Room Cleanup For His Motel To Duffy's Maid Service. Tim rents an average of 50 rooms for each of 365 nights (365 x 50 equals the total rooms rented for year). Tim's cost to clean a room is $12.50. The Duffy's Maid Service quote is $18.00 per room plus a fixed cost of $26,000 for sundry items such as uniforms with the motel's name. Tim's annual fixed cost for space, equipment, and supplies is $ 61,000.

Based on the given information related to costs for each of the options, the crossover point for Tim =­­­­____ room nights.
If the number of room nights is less than the crossover point, then ______ is the best option avaliable to Tim.
Based on the given room nights that Tim expects to rent (18,250), the best option is ____

Answer 1

The crossover point occurs at 6,363.64 room nights. Since Tim expects to rent 18,250 room nights annually, outsourcing the cleaning services to Duffy's Maid Service is the best option.

Step-by-step explanation:

The crossover point is when the costs of cleaning rooms internally equal the costs of outsourcing the cleanup. To find the crossover point, we need to compare two cost equations - the cost of internal cleaning and the cost of outsourcing to Duffy's Maid Service:

Cost of Internal Cleaning: Total cost = Fixed Cost + (Variable Cost per Room x Number of Rooms)
Cost of Outsourcing: Total cost = Fixed Cost + (Cost per Room x Number of Rooms)

For Tim's internal cleaning, the fixed cost is $61,000 and the variable cost is $12.50 per room. Duffy's fixed cost is $26,000 and the cost per room is $18.00.

The equations are:

• Internal: $61,000 + $12.50x
• Duffy's: $26,000 + $18.00x

By equating the two:

$61,000 + $12.50x = $26,000 + $18.00x

$61,000 - $26,000 = $18.00x - $12.50x

$35,000 = $5.50x

x = $35,000 / $5.50

x = 6,363.64

Since Tim rents an average of 50 rooms for 365 nights, totaling 18,250 room nights a year, we compare this to the crossover point. If Tim's annual room nights are less than 6,363.64, then internal cleaning is the best option; if more, outsourcing is the better option.

As 18,250 is higher than 6,363.64, outsourcing the cleaning services to Duffy's Maid Service is the best option for Tim.