Question

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 $16 per day. Clyde has 2 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 $16 mentioned as profit is instead the excess cost per day for each machine and that the shortage cost is unknown. Assuming that the optimal number of machines is 2, what is the implied range of shortage cost per machine? (Enter smaller value in first box and larger value in second box. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.)

Implied range of shortage cost per machine from $ ____ to $ ____

Answer 1

Answer:

a) Calculate the cumulative frequency for the demand data as follows

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	1.00
Total	1.00

Shortage cost per unit(c_s) = $16 per machine

Total no of rug cleaning machines(n) = 2

the formula to calculate service level(SL) is shown below

SL = c_{s /} c_{s +} c_e

Determine the value of C_e for service level greater than 0.85 as follows:

16/16 + c_e> 0.85

c_e<   2.82

Determine the value of C_e for service level greater than 0.95 as follows:

16/16 + c_e> 0.95

c_e<   0.84

Hence the optimal range c_e should be between 0.84 and 2.82

b)

The excess cost per machine would increase with increase in number of excess inventories. therefore compnay C would reduce the number of rug machines he stocks to avoid the excess inventory costs

c)

Determine the value c_s for service level greater than 0.85 as follows

c_s / c_s + 16 > 0.85

c_s> 90.67

Determine the value c_s for service level greater than 0.95 as follows

c_s / c_s + 16 > 0.95

c_s> 294.4

Hence the optimal range of c_s should be between 90.67 and 294.4