The owner of a motel is considering outsourcing the daily room cleanup to Duffy’
ID: 361807 • Letter: T
Question
The owner of a motel is considering outsourcing the daily room cleanup to Duffy’s Maid Service. The manager rents an average of 50 rooms for each of 365 nights. The owner’s cost to clean a room is $12. The Duffy’s Maid Service quote is $18 per room plus a fixed cost of $24,000 for sundry items such as uniforms with the motel’s room. The owner’s fixed cost for space, equipment, and supplies is $60,000.
(a) Determine the crossover point for the two options. Please give the formula for calculating crossover points, at least one step of calculation, and the correct answer for full credit. (6 points)
(b) Which option should be chosen and why? (4 points)
Explanation / Answer
Total cost for any party ( i.e owner or Duffys) = Fixed cost + Total variable cost
Let the crossover point in terms of number of rooms to be rent out per day = N
Cost for owners for cleaning N rooms per day :
Fixed cost for owners = $ 60,000
Total variable cost = $12 / room x N rooms/ day x 365 days = $4380.N
Hence total cost for owners = $ 60000 + $4380.N
Cost for Duffy’s maid service :
Fixed cost = $24,000
Total variable cost = $18/ room x N rooms/ day x 365 days =$6570.N
Hence, total cost for Duffy’s maid service = 24000 + 6570.N
For Duffy’s maid service to be chosen, its total cost should be less than total cost to be incurred by owners.
Which means :
24000 + 6570.N < 60000 + 4380.N
Or, 2190.N < 36000
Or, N < 16.43
Answer to question a :
Therefore , crossover point for two options is 16.43 rooms per day which means:
If number of rooms to be cleaned is 16 or less , Duffy’s maid service should be chosen
If number of rooms to be cleaned is 17 or more, In house operation option should be chosen
Answer to question b :
Since the manager rents out on average 50 rooms each day which is in the category of “ 17 rooms or more” , inhouse operation option should be chosen and Duffy’s maid service should not be hired
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