Question

Time 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 and average of 50 rooms for each of 365 nights (365 x 50 equals the total rooms rented for the year). Tim’s cost to clean a room is $13.50. The Duffy’s Maid Service quote is $18.50 per room plus a fixed cost of $25,000 for sundry items such as uniforms with the motel’s name Tims annual fixed cost for space, equipment and supplies is $65,000


based on the given information realated to costs for each of the options, the cross over point for tim is = _____

Answer 1

Answer:

The indifference point is 8,000 rooms.

Explanation:

Giving the following information:

Tim’s cost to clean a room is $13.50. The Duffy’s Maid Service quote is $18.50 per room plus a fixed cost of $25,000 for sundry items such as uniforms with the motel’s name Tims annual fixed cost for space, equipment and supplies is $65,000

Tim= 65,000 + 13.50*x

Duffy= 25,000 + 18.5*x

65,000 + 13.5x= 25,000 + 18.5x

40,000=5x

8,000 = x

The indifference point is 8,000 rooms.

In days= 8,000/50= 160 days

Answer 2

The cross-over point is 8,000 rooms.

• Based on the information given in the question, let the cross-over point be represented by x.

• Then, the equation to solve the question goes thus:

Tim has an equation of:

= 65,000 + (13.50 × x)

= 65000 + 13.50x

• Duffy has an equation of:

= 25,000 + (18.5 × x)

= 25000 + 18.5x

We then equate both equations which will be:

65,000 + 13.5x= 25,000 + 18.5x

Collect like terms

18.5x - 13.5x = 65000 - 25000

5x = 4000

x = 40000/5

x = 8000

Therefore, indifference or cross-over point is 8,000 rooms.

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