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

Answer:

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

Step-by-step 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

        $h = \frac{r - x}{k- y}$

substituting values

      $h = \frac{61000 - 25000}{ 18 - 12.5}$

      $h = 6545 \ room \ nights$