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Chapter 6- Solved Problems
Problem 1
Customers arrive at a bank drive-up window every 3.5 minutes based on a Poisson
distribution. Once they arrive at the teller, service time is exponentially distributed based
on a rate of 4 minutes per transaction,
a. What is the probability that a customer will not have to wait for service?
b. How many customers are most likely in line (waiting) at any one point in
time?
c. What will be the average time waiting in the system?
d. What will be the average time in the system?
Answer Problem 1
T n  T = 12.5%
A. Pn 
n!
B. Cw 
2
= 6.125 people
    
C. Tw 

= 1.75 min
    
D. Ts 
1
= 2 min
 
Problem 2
A company is selecting among three alternative capacity plans. The first alternative is a
job shop with low fixed costs ($250,000), but with highly skilled labor higher variable
cost per unit ($18). The second alternative is a form of cellular manufacturing with fixed
cost of $325,000 and variable cost of $14 per unit. The third consideration is a product
layout. This will cost $500,000 to set up, but result in a variable cost of only $7.50 per
unit. Which layout should be selected at the following volumes (a) 10,000, (b) 20,000 ,
(c) 30,000.
Answer Problem 2
Job vs. Cell
250,000 + 18X = 325,000 + 14X
X = 18,750
Cell vs. Product
325,000 + 14X = 500,000 + 7.5X
X = 26,923.07
A. A job shop is best at 10,000 units
B. A cell would be best for 20,000 units
C. A product layout would be best for 30,000 units
Problem 3
A beverage supply company is trying to determine the appropriate stocking level for an
upcoming festival to be held in town. Based on historic data, the company predicts that
there is a 30% chance that the festival will attract 20,000 customers (small); a 40%
chance that it will attract 45,000 (medium); a 20% chance that it will attract 60,000
(large); and a 10% chance it will attract 75,000 (huge). Assuming that each customer
represents one sale of $5, what is the value of the festival for the company?
Answer Problem 3
Size
Small
Medium
Large
huge
EMV = $217,500
Probability
.30
.40
.20
.10
Customers
20000
45000
60000
75000
Value
30000
90000
60000
37500