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 × 50 equals the total rooms rented for the​ 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 $25,000 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 Time​ = _______nothing room nights ​(round your response to the nearest whole ​number).

Answer 1

The crossover point for Time​
`h = 6545 \ room \ nights`

Explanation:

From the question we are told that

The total rooms rented for the year is
`z = 50 * 365 = 18250 \ rooms`

Time's fixed cost is r = $61,000

Time's variable cost is
`y =`$12.5 per room

Duffy's Maid Service fixed cost is
`x =`$25,000

Duffy's Maid Service variable cost is
`k =` $18.00 per room

The cross over point for Time is mathematically represented as

`h = (r - x)/(k- y)`

substituting values

`h = (61000 - 25000)/( 18 - 12.5)`

`h = 6545 \ room \ nights`