Problem 13-40 Demand for rug-cleaning machines at Clyde’s U-Rent-It is shown in
ID: 447977 • Letter: P
Question
Problem 13-40
Demand for rug-cleaning machines at Clyde’s U-Rent-It is shown in the following table. Machines are rented by the day only. Profit on the rug cleaners is $13 per day. Clyde has four rug-cleaning machines.
Demand Frequency 0 .30 1 .20 2 .20 3 .15 4 .10 5 .05 1.00
a. Assuming that Clyde’s stocking decision is optimal, what is the implied range of excess cost per machine? (Enter smaller value in first box and larger value in second box. Do not round intermediate calculations. Round your answers to 2 decimal places.
Omit the "$" sign in your response.) Implied range of excess cost per machine from $ to $
b. Your answer from part a has been presented to Clyde, who protests that the amount is too low. Does this suggest an increase or a decrease in the number of rug machines he stocks? Increase Decrease
c. Suppose now that the $13 mentioned as profit is instead the excess cost per day for each machine and that the shortage cost is unknown. Assuming that the optimal number of machines is four, what is the implied range of shortage cost per machine? (Enter smaller value in first box and larger value in second box. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.)
Implied range of shortage cost per machine from $ to $
Explanation / Answer
Demand for rug cleaning machines is shown in the table below. Machines are rented by the day only. Profit on rug cleaners = $13 /day. Clyde has 4 rug-cleaning machines.
a. Determine the implied range of excess cost per machine:
S0 = 4
Cs = $13
Ce = unknown
For 4 machines to be optimal, the SL ratio must be .85 and .95.
Step 1: Set SL = .85 and solve for Ce :
SL = Cs / (Cs +Ce)
0.85 = 13 / (13 +Ce)
Ce =$ 2.29
Set SL = .95 and solve for Ce :
SL = Cs / (Cs +Ce)
0.95 = 13 / (13 +Ce)
Ce =$ 0.69
Conclusion: Implied range of excess cost: $.69 $ 2.29.
b. Your answer from part a has been presented to Clyde, who protests that the amount is too low. Does this suggest an increase or a decrease in the number of rug machines he stocks? Increase Decrease
Answer :
If the surplus cost is supposed to be senior, then the number of equipment should be reduce. When excess cost add to, SL decreases along with the best stocking level.
c. Suppose now that the $13 mentioned as profit is instead the excess cost per day for each machine and that the shortage cost is unknown. Assuming that the optimal number of machines is four, what is the implied range of shortage cost per machine?
Answer :
S0 = 4
Cs = unknown
Ce = $10
Set SL = .85 and solve for Cs :
SL = Cs / (Cs +Ce)
0.85 = Cs / (Cs +10)
Cs =73.66
Set SL = .95 and solve for Ce :
SL = Cs / (Cs +Ce)
0.95 = Cs / (Cs +13)
Cs =$ 247
Conclusion: Implied range of shortage cost: $73.66 $247
Demand Frequency Cumulative Frequency 0 0.30 0.30 1 0.20 0.50 2 0.20 0.70 3 0.15 0.85 4 0.10 0.95 5 0.05 1