I keep getting the wrong answer for part c. Problem 13-40 Demand for rug-cleanin

Question

I keep getting the wrong answer for part c.

Problem 13-40 Demand for rug-cleaning machines at Clyde's U-Rent-lt 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 $ 8.57 to 20 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 $20 mentioned as profit is instead the excess cost per day for each machine and that the shortage cost is unknown. Assuming that the optimal number of machines is four, what is the implied range of shortage cost per machine? (Enter smaller value in first box and larger value In second box. Do not round Intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.) Implied range of shortage cost per machine from$ to $

Explanation / Answer

a)

Underage cost, Cu = 20 (profit per machine)

Corresponding to demand of 2 machines, the cumulative frequency range is 0.3+0.2 = 0.5 to 0.3+0.2+0.2 = 0.7

So, range of critical ratio Cu/(Cu+Co) = 0.5 to 0.7 (Co is overage or excess cost)

Lower limit of critical ratio, Cu/(Cu+Co) = 20/(20+Co) = 0.5   

or, Co = 20

Upper limit of critical ratio, Cu/(Cu+Co) = 20/(20+Co) = 0.7

or, Co = 8.57

Implied range of excess cost per machine from $ 8.57 to $ 20

b) Decrease

Clyde's protest suggests that the actual value of Co shuld be higher than 20. Therefore, critical ratio will be even lower than 0.5, hence the corresponding number of machines should decrease.

c) Now, given that, Co = 20 and Cu = ?

For optimal number of machines equal to 4, the implied range of critical ratio is 0.3+0.2+0.2+0.15 = 0.85 to  0.3+0.2+0.2+0.15+0.1 = 0.95

Lower limit of critical ratio, Cu/(Cu+Co) = Cu/(Cu+20) = 0.85  

or, Cu = 113.33

Upper limit of critical ratio, Cu/(Cu+Co) = Cu/(Cu+20) = 0.95

or, Cu = 380

Implied range of shortage cost per machine from $ 113.33 to $ 380

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