Quantitative Analysis
BA 452 Homework 3 Questions
27.
Golf Shafts,
Inc. (GSI), produces graphite shafts for several manufacturers of golf clubs.
Two GSI manufacturing facilities, one located in San Diego and the other in
Tampa, have the capability to produce shafts in varying degrees of stiffness,
ranging from regular models used primarily by average golfers to extra stiff
models used primarily by lowhandicap and professional golfers. GSI just
received a contract for the production of 200,000 regular shafts for previous
orders, neither plant has sufficient capacity by itself to fill the new order.
The San Diego plant can produce up to a total of 180,000 shafts. Because the
equipment differences at each of the plants and differing labor costs, the
perunit production costs vary as shown here:

San Diego
Cost

Tampa Cost

Regular
shaft

$5.25

$4.95

Stiff
shaft

$5.45

$5.70




a.
Formulate a
linear programming model to determine how GSI should schedule production for
the new order in order to minimize the total production cost.
b. Solve the model that you developed in part (a).
c. Suppose that some of the previous orders at the
Tampa plant could be rescheduled in order to free up additional capacity for
the new order. Would this option be worthwhile? Explain.
d.
Suppose
that the cost to produce a stiff shaft in Tampa had been incorrectly computed,
and that the correct cost is $5.30 per shaft. What effect, if any, would the
correct cost have on the optimal solution developed in part (b)? What effect
would it have on the total production cost?
Quantitative
Analysis BA 452 Homework 3 Questions
28.
The
Pfeiffer Company manages approximately $15 million for clients. For each
client, Pfeiffer choose a mix of three investment vehicles: a growth stock
fund, an income fund, and a money market fund. Each client has different
investment objectives and different tolerances for risk. To accommodate these
differences, Pfeiffer places limits on the percentage of each portfolio that
may be invested in the three funds and assigns a portfolio risk to each client.
Here’s how the system works for Dennis Hartman,
one of Pfeiffer’s clients. Based on an evaluation of Hartmann’s risk tolerance,
Pfeiffer has assigned Hartmann’s portfolio a risk index of 0.05. Furthermore,
to maintain diversity, the fraction of Hartmann’s portfolio invested in the
growth and income funds must be at least 10% for each, and at least 20% must be
in the money market fund.
The risk ratings for the growth, income, and money market funds are
0.10, 0.05, and 0.01, respectively. A portfolio risk index is computed as a
weighted average of the risk ratings for the three funds where the weights are
the fraction of the portfolio invested in each of the funds. Hartmann has given
Pfeiffer $300,000 to manage. Pfeiffer is currently forecasting a yield of 20%
growth fund, 10% on the income fund, and 6% on the money market fund.
a.
Develop a
linear programming model to select the best mix of investments for Hartmann’s
portfolio.
b. Solve the model you developed in part (a).
c.
How much
may the yields on the three funds vary before it will be necessary for Pfeiffer
to modify Hartmann’s portfolio?
d. If Hartmann were more risk tolerant, how much of
a yield increase could be expect? For instance, what if his portfolio risk
index is increased to 0.06?
e. If Pfeiffer revised the yield estimate for the
growth fund downward to 0.10, how would you recommend modifying Hartmann’s
portfolio?
f.
What
information must Pfeiffer maintain on each client in order to use this system
to manage client portfolios?
g.
On a weekly
basis Pfeiffer revises the yield estimates for the three funds. Suppose
Pfeiffer has 50 clients. Describe how you would envision Pfeiffer making weekly
modifications in each client’s portfolio and allocating the total funds managed
among the three investment funds.
Quantitative
Analysis BA 452 Homework 3 Questions
29.
La Jolla
Beverage Products is considering producing a wine cooler that would be a blend
of white wine, a rose wine, and fruit juice. To meet taste specifications, the
wine cooler must consist of at least 50% white wine, at least 20% and no more
than 30% rose wine, and exactly 20% fruit juice. La Jolla purchases wine from
local wineries and the fruit juice from a processing plant in San Francisco.
For the current production period, 10,000 gallons of white wine and 8,000
gallons of rose wine can be purchased; an unlimited amount of fruit juice can
be ordered. The costs for the wine are $1.00 per gallon for the white and $1.50
per gallon for the rose; the fruit juice can be purchased for $0.50 per gallon.
La Jolla Beverage Products can sell all of the wine cooler they produce for
$2.50 per gallon.
a. Is the cost of the wine and fruit juice a sunk
cost or a relevant cost in this situation? Explain.
b.
Formulate a
linear program to determine the blend of the three ingredients that will
maximize the total profit contribution. Solve the linear program to determine
the number of gallons of each ingredient La Jolla should purchase and the total
profit contribution they will realize from this blend.
c.
If La Jolla
could obtain additional amounts of the white wine, should they do so? If so,
how much should they be willing to pay for each additional gallon, and how many
additional gallons would they want to purchase?
d.
If La Jolla
Beverage Products could obtain additional amounts of the rose wine, should they
do so? If so, how much should they be willing to pay for each additional
gallon, and how many additional gallons would they want to purchase?
e.
Interpret
the dual value for the constraint corresponding to the requirement that the
wine cooler must contain at least 50% white wine. What is your advice to
management given this dual value?
f.
Interpret
the dual value for the constraint corresponding to the requirement that the
wine cooler must contain exactly 20% fruit juice. What is your advice to
management given this dual value?
Quantitative
Analysis BA 452 Homework 3 Questions
30.
The program
manager for Channel 10 would like to determine the best way to allocate the
time for the 11:0011:30 evening news broadcast. Specifically, she would like
to determine the number of minutes of broadcast time to devote to local news,
national news, weather, and sports. Over the 30minute broadcast, 10 minutes
are set aside for advertising. The station’s broadcast policy states that at
least 15% of the time available should be devoted to local news coverage; the
time devoted to local news or national news must be at least 50% of the total
broadcast time; the time devoted to the weather segment must be less than or
equal to the time devoted to the sports segment; the time devoted to the sports
segment should be no longer than the total time spent on the local and national
news; and at least 20% of the time should be devoted to the weather segment.
The production costs per minute are $300 for local news, $200 for national
news, $100 for weather, and $100 for sports.
a.
Formulate
and solve a linear program that can determine how the 20 available minutes
should be used to minimize the total cost of producing the program.
b. Interpret the dual value for the constraint
corresponding to the available time. What advice would you give the station
manager given this dual value?
c.
Interpret
the dual value for the constraint corresponding to the requirement that at
least 15% of the available time should be devoted to local coverage. What
advice would you give the station manager given this dual value?
d.
Interpret
the dual value for the constraint corresponding to the requirement that the
time devoted to the local and the national news must be at least 50% of the
total broadcast time. What advice would you give the station manager given this
dual value?
e.
Interpret
the dual value for the constraint corresponding to the requirement that the
time devoted to the weather segment must be less than or equal to the time
devoted to the sports segment. What advice would you give the station manager
given this dual value?
Quantitative
Analysis BA 452 Homework 3 Questions
31.
Gulf Coast
Electronics is ready to award contracts for printing their annual report. For
the past several years, the fourcolor annual report has been printed by
Johnson Printing and Lakeside Litho. A new firm, Benson Printing, inquired into
the possibility of doing a portion of the printing. The quality and service
level provided by Lakeside Litho has been extremely high; in fact, only 0.5% of
their reports have had to be discarded because of quality problems. Johnson
Printing has also had a high quality level historically, producing an average
of only 1% unacceptable reports. Because Gulf Coast Electronics has had no
experience with Benson Printing, they estimated their defective rate to be 10%.
Gulf Coast would like to determine how many reports should be printed by each
firm to obtain 75,000 acceptablequality reports. To ensure that Benson
Printing will receive some of the contract, management specified that the
number of reports awarded to Benson Printing must be at least 10% of the volume
given to Johnson Printing. In addition, the total volume assigned to Benson
Printing, Johnson Printing, and Lakeside Litho should not exceed 30,000,
50,000, and 50,000 copies, respectively. Because of the longterm relationship
with lakeside Litho, management also specified that at least 30,000 reports
should be awarded to Lakeside Litho. The cost per copy is $2.45 for Benson
Printing, $2.50 for Johnson Printing, and $2.75 for Lakeside Litho.
a.
Formulate
and solve a linear program for determining how many copies should be assigned
to each printing firm to minimize the total cost of obtaining 75,000 acceptable
quality reports.
b. Suppose that the quality level for Benson
Printing is much better than estimated. What effect, if any, would this quality
level have?
c.
Suppose that
management is willing to reconsider their requirement that the Lakeside Litho
be awarded at least 30,000 reports. What effect, if any, would this
consideration have?
Quantitative Analysis
BA 452 Homework 3 Questions
32.
PhotoTech,
Inc., a manufacturer of rechargeable batteries for digital cameras, signed a
contract with a digital photography company to produce three different
lithiumion battery packs for a new line of digital cameras. The contract calls
for the following:
Battery Pack

Production Quantity



PT100

200,000



PT200

100,000



PT300

150,000



PhotoTech can manufacture the battery packs at
manufacturing plants located in the Philippines and Mexico. The unit cost of
the battery packs differs at the two plants because of differences in
production equipment and wage rates. The unit costs for each battery pack at
each manufacturing plant are as follows:
.gif">.gif">.gif">
Plant
.gif">
Product

Philippines

Mexico




PT100

$0.95

$0.98




PT200

$0.98

$1.06




PT300

$1.34

$1.15




The PT100 and PT200 battery packs are produced using similar
production equipment available at both plants. However, each plant has a
limited capacity for the total number of PT100 and PT200 battery packs
produced. The combined PT100 and PT200 production capacities are 175,000
units at the Philippines plant and 160,000 units at the Mexico plant. The
PT300 production capacities are 75,000 units at the Philippines plant and
100,000 units at the Mexico plant. The cost of shipping from the Philippines
plant is $0.18 per unit, and the cost of shipping from the Mexico plant is
$0.10 per unit, and the cost of shipping from the Mexico plant is $0.10 per
unit.
a. Develop a linear program that PhotoTech can use
to determine how many units of each battery pack to produce at each plant in
order to minimize the total production and shipping cost associated with the
new contract.
b. Solve the linear program developed in part (a) to
determine the optimal production plan.
c.
Use
sensitivity analysis to determine how much the production and/or shipping cost
per unit would have to change in order to produce additional units of the
PT100 in the Philippines plant.
d.
Use
sensitivity analysis to determine how much the production and/or shipping cost
per unit would have to change in order to produce additional units of the
PT200 in the Mexico plant.