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Details: Read modules A, C, and D in Part 4: Business Analytics Modules.
Problems Note: PX means the problemmay be solved with POM for Windows and/or Excel OM.
Complete problems 14.8 and 14.9 in the textbook.
Submit one Excel file. Put each problem result on a separate sheet in your file.
14.8As the production planner for Scott Sampson
Products, Inc., you have been given a bill of material for a bracket
that is made up of a base, two springs, and four clamps. The base
is assembled from one clamp and two housings. Each clamp has
one handle and one casting. Each housing has two bearings and
one shaft. There is no inventory on hand.
a) Design a product structure noting the quantities for each item
and show the low-level coding.
b) Determine the gross quantities needed of each item if you are
to assemble 50 brackets.
c) Compute the net quantities needed if there are 25 of the base
and 100 of the clamp in stock. PX
14.9Your boss at Scott Sampson Products, Inc., has just
provided you with the schedule and lead times for the bracket in
Problem 14.8. The unit is to be prepared in week 10. The lead
times for the components are bracket (1 week), base (1 week),
spring (1 week), clamp (1 week), housing (2 weeks), handle
(1 week), casting (3 weeks), bearing (1 week), and shaft (1 week).
a) Prepare the time-phased product structure for the bracket.
b) In what week do you need to start the castings? PX
Details:
Complete problems B.1, B.5, B.7, B.11, and B.21 in the textbook.
Submit one Excel file. Put each problem result on a separate sheet in your file.
B.1Solve the following linear programming problem
graphically:
Maximize profit = 4X + 6Y
Subject to: X + 2Y … 8
5X + 4Y … 20
X, Y U 0
B.5Solve the following LP problem graphically:
Minimize cost = 24X + 15Y
Subject to: 7X + 11Y U 77
16X + 4Y U 80
X, Y U 0
B.7The Attaran Corporation manufactures two electrical
products: portable air conditioners and portable heaters. The
assembly process for each is similar in that both require a certain
PX
B.11The Sweet Smell Fertilizer Company markets bags
of manure labeled “not less than 60 lb dry weight.” The packaged
manure is a combination of compost and sewage wastes. To
provide good-quality fertilizer, each bag should contain at least
30 lb of compost but no more than 40 lb of sewage. Each pound
of compost costs Sweet Smell 5¢ and each pound of sewage costs
4¢. Use a graphical LP method to determine the least-cost blend
of compost and sewage in each bag. PX
B.21. Par, Inc., produces a standard golf bag and a deluxe
golf bag on a weekly basis. Each golf bag requires time for cutting
and dyeing and time for sewing and finishing, as shown in the following
table:
|
HOURS REQUIRED PER BAG
|
|
PRODUCT
|
CUTTING AND DYEING
|
SEWING AND FINISHING
|
|
STANDARD BAG
|
½
|
1
|
|
DELUXE BAG
|
1
|
2/3
|
HOURS REQUIRED PER BPRODUCT CUTTING AND DYEING SEWING AND FINISHING
The profits per bag and weekly hours available for cutting and
dyeing and for sewing and finishing are as follows:
|
PRODUCT
|
PROFIT PER UNIT ($)
|
|
STANDARD BAG
|
10
|
|
DELUXE BAG
|
8
|
PRODUCT PROFIT PER UNIT ($)
|
ACTIVITY
|
WEEKLY HOURS AVAILABLE
|
|
CUTTING AND DYEING
|
300
|
|
SEWING AND FINISHING
|
360
|
ACTIVITY WEEKLY HOURS AVAILABLE
Par, Inc., will sell whatever quantities it produces of these two
products.
a) Find the mix of standard and deluxe golf bags to produce per
week that maximizes weekly profit from these activities.
b) What is the value of the profit? PX
Details:
Complete problems D.1, D.3, D.6, and D.8 in the textbook.
Submit one Excel file. Put each problem result on a separate sheet in your file.
D.1Customers arrive at Rich Dunn’s Styling Shop at a
rate of 3 per hour, distributed in a Poisson fashion. Rich can perform
haircuts at a rate of 5 per hour, distributed exponentially.
a) Find the average number of customers waiting for haircuts.
b) Find the average number of customers in the shop.
c) Find the average time a customer waits until it is his or her turn.
d) Find the average time a customer spends in the shop.
e) Find the percentage of time that Rich is busy. PX
D.3Paul Fenster owns and manages a chili-dog and softdrink
stand near the Kean U. campus. While Paul can service 30
customers per hour on the average (m), he gets only 20 customers
per hour (l). Because Paul could wait on 50% more customers
than actually visit his stand, it doesn’t make sense to him that he
should have any waiting lines.
Paul hires you to examine the situation and to determine
some characteristics of his queue. After looking into the problem,
you find it follows the six conditions for a single-server waiting
line (as seen in Model A). What are your findings? PX
D.6Calls arrive at Lynn Ann Fish’s hotel switchboard at
a rate of 2 per minute. The average time to handle each is 20 seconds.
There is only one switchboard operator at the current time.
The Poisson and exponential distributions appear to be relevant
in this situation.
a) What is the probability that the operator is busy?
b) What is the average time that a customer must wait before
reaching the operator?
c) What is the average number of calls waiting to be answered?
PX
D.8Virginia’s Ron McPherson Electronics Corporation
retains a service crew to repair machine breakdowns that occur
on average l = 3 per 8-hour workday (approximately Poisson in
nature). The crew can service an average of m = 8 machines per
workday, with a repair time distribution that resembles the exponential
distribution.
a) What is the utilization rate of this service system?
b) What is the average downtime for a broken machine?
c) How many machines are waiting to be serviced at any given
time?
d) What is the probability that more than 1 machine is in the
system? The probability that more than 2 are broken and
waiting to be repaired or being serviced? More than 3? More
than 4? PX
