Problem 13-40 Demand for rug-cleaning machines at Clyde\'s U-Rent-It is shown in
ID: 425098 • 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 $20 per day. Clyde has 2 rug-cleaning machines. Demand Frequency- .30 .20 .20 .15 .10 .05 1.00 a. Assuming that Clyde's stocking decision is optimal, what is the implied range of excess cost per machine? (Enter smaller value in first box and larger value in second box. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.) implied range of excess cost per machine from $ Dwww] 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?Explanation / Answer
Cs = shortage cost = $20 (opportunity loss)
Ce = excess cost (unknown)
(a)
Since they have 2 machines, the optimum service level should range from 0.50 to 0.70 and the corresponding equality with the critical ratio gives,
20 / (20 + Ce) = 0.50 --------(1)
20 / (20 + Ce) = 0.70 --------(2)
Solving (1) and (2), the two values of Ce are found as 20 and 8.57. So, the implied range is from $8.57 to $20.
(b)
At optimality, critical ratio = Cs / (Cs + Ce) = Service level
If Ce from the above calculation is found very small, then, in reality, it is larger. This would imply a reduction in optimum service level or a decrease in the number of machines.
Demand Prob CumProb 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 1.00