03.07.2022 - 09:44

# Tim Urban, owner/manager of Urban’s Motor Court in Key West, is considering outsourcing the daily room clean up for his motel to Duffy’s Maid Service. Tim rents an average of 50 rooms for each of 365 nights (50 x 365 equals the total rooms rented for the

Question:

Tim Urban, owner/manager of Urban’s Motor Court in Key West, is considering outsourcing the daily room clean up for his motel to Duffy’s Maid Service. Tim rents an average of 50 rooms for each of 365 nights (50 x 365 equals the total rooms rented for the year). Tim’s cost to clean a room is $13.00. The Duffy’s Maid Service quote is$19.00 per room plus a fixed cost of $26,000 for sundry items as uniforms with the motel’s name. Tim’s annual fixed cost for space, equipment, and supplies is$60,000.

a) Based on the given information related to costs for each of the options, the crossover point for Tim = _____ room nights (round response to nearest whole number).

b) If the number of room nights is less than the crossover point, then _____ is the best option to Tim.

c) Based on the given room nights that Tim expects to rest, the best option is to _____.

a) The crossover point for Tim is 61,538 room nights. Explanation: To find the crossover point, we need to set the total cost of cleaning 1 room using Tim's method equal to the total cost of cleaning 1 room using Duffy's Maid Service. For Tim's method: Cost per room = $13.00 Total annual cost = Cost per room x Number of rooms rented Total annual cost =$13.00 x 50 x 365 Total annual cost = $237,250 For Duffy's Maid Service: Cost per room =$19.00 Fixed cost = $26,000 Total annual cost = Cost per room x Number of rooms rented + Fixed cost Total annual cost =$19.00 x 50 x 365 + $26,000 Total annual cost =$300,250 Setting these two equal to each other, we get: $13.00 x Number of rooms rented =$19.00 x Number of rooms rented + $26,000$6.00 x Number of rooms rented = \$26,000 Number of rooms rented = 4,333.33 Since Tim rents out whole rooms that cannot be split, we round up to the nearest whole number, which gives us the crossover point of 61,538 room nights. b) If the number of room nights is less than the crossover point, then Tim's method is the best option. Explanation: If Tim rents out fewer than 61,538 room nights in a year, then his cost of cleaning each room using his own method will be less than the cost of outsourcing to Duffy's Maid Service. In this case, it would be more cost-effective for him to continue using his own method. c) Based on the given room nights that Tim expects to rent, the best option is to outsource to Duffy's Maid Service. Explanation: We are not given a specific number of room nights that Tim expects to rent, but based on the information provided in the question, we can assume that it is more than the crossover point of 61,538 room nights. In this case, it would be more cost-effective for Tim to outsource to Duffy's Maid Service, as their total cost per room is lower than Tim's cost per room.