false

Study Guides
(248,683)

Canada
(121,693)

York University
(10,209)

Administrative Studies
(1,427)

ADMS 3330
(38)

Michael Gadsden
(2)

School

York University
Department

Administrative Studies

Course Code

ADMS 3330

Professor

Michael Gadsden

Description

9. Linear Programming Applications in
Marketing, Finance, and Operations Management
MULTIPLE CHOICE
1. Media selection problems usually determine
a. how many times to use each media source.
b. the coverage provided by each media source.
c. the cost of each advertising exposure.
d. the relative value of each medium.
ANSWER: a
TOPIC: Media selection
2. To study consumer characteristics, attitudes, and preferences, a company
would engage in
a. client satisfaction processing.
b. marketing research.
c. capital budgeting.
d. production planning.
ANSWER: b
TOPIC: Marketing research
3. A marketing research application uses the variable HD to represent the
number of homeowners interviewed during the day. The objective function
minimizes the cost of interviewing this and other categories and there is a
constraint that HD > 100. The solution indicates that interviewing another
homeowner during the day will increase costs by 10.00. What do you know?
a. the objective function coefficient of HD is 10.
b. the dual price for the HD constraint is 10.
c. the objective function coefficient of HD is -10.
d. the dual price for the HD constraint is -10.
ANSWER: d
TOPIC: Marketing research
4. The dual price for a constraint that compares funds used with funds available
is .058. This means that
a. the cost of additional funds is 5.8%.
b. if more funds can be obtained at a rate of 5.5%, some should be.
c. no more funds are needed.
d. the objective was to minimize.
ANSWER: b
TOPIC: Portfolio selection
1 2 Chapter 9 Linear Programming Applications
5. Let M be the number of units to make and B be the number of units to buy. If
it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed,
the objective function is
a. Max 2M + 3B
b. Min 4000 (M + B)
c. Max 8000M + 12000B
d. Min 2M + 3B
ANSWER: d
TOPIC: Make or buy
6. If Pij the production of product i in period j, then to indicate that the limit on
production of the company’s three products in period 2 is 400,
a. P 21+ P 22+ P 23 < 400
b. P 12+ P 22+ P 32 < 400
c. P 32< 400
d. P 23< 400
ANSWER: b
TOPIC: Production scheduling
7. Let P ijthe production of product i in period j. To specify that production of
product 1 in period 3 and in period 4 differs by no more than 100 units,
a. P 13- P14 < 100; P14- P13 < 100
b. P 13- P14 < 100; P13- P14 > 100
c. P 13- P14 < 100; P14- P13 > 100
d. P 13- P14 > 100; P14- P13 > 100
ANSWER: a
TOPIC: Production scheduling
8. Let A, B, and C be the amounts invested in companies A, B, and C. If no more
than 50% of the total investment can be in company B, then
a. B < 5
b. A - .5B + C < 0
c. .5A - B - .5C < 0
d. -.5A + .5B - .5C < 0
ANSWER: d
TOPIC: Portfolio selection
9. Department 3 has 2500 hours. Transfers are allowed to departments 2 and
4, and from departments 1 and 2. If A measures the labor hours allocated to
i
department i and T theijours transferred from department i to department j,
then
a. T + T - T - T - A = 2500
13 23 32 34 3
b. T 31+ T 32- T23 - T43+ A 3 2500
c. A 3 T 13 + T 23- T32- T34 = 2500
d. A 3 T 13 - T23+ T 32+ T 34 = 2500
ANSWER: d
TOPIC: Work force assignment
10. Modern revenue management systems maximize revenue potential for an
organization by helping to manage Chapter 9 Linear Programming Applications 3
a. pricing strategies.
b. reservation policies.
c. short-term supply decisions.
d. All of the alternatives are correct.
ANSWER: d
TOPIC: Revenue management
TRUE/FALSE
1. Media selection problems can maximize exposure quality and use number of
customers reached as a constraint, or maximize the number of customers
reached and use exposure quality as a constraint.
ANSWER: True
TOPIC: Media selection
2. Revenue management methodology was originally developed for the banking
industry.
ANSWER: False
TOPIC: Revenue management
3. Portfolio selection problems should acknowledge both risk and return.
ANSWER: True
TOPIC: Portfolio selection
4. If an LP problem is not correctly formulated, the computer software will
indicate it is infeasible when trying to solve it.
ANSWER: False
TOPIC: Computer solutions
5. It is improper to combine manufacturing costs and overtime costs in the
same objective function.
ANSWER: False
TOPIC: Make-or-buy
6. Production constraints frequently take the form:
beginning inventory + sales - production = ending inventory
ANSWER: False
TOPIC: Production scheduling
7. If a real-world problem is correctly formulated, it is not possible to have
alternative optimal solutions.
ANSWER: False
TOPIC: Problem formulation
8. To properly interpret dual prices, one must know how costs were allocated in
the objective function.
ANSWER: True 4 Chapter 9 Linear Programming Applications
TOPIC: Make-or-buy
9. A company makes two products from steel; one requires 2 tons of steel and
the other requires 3 tons. There are 100 tons of steel available daily. A
constraint on daily production could be written as: 2x1 + 3x2 < 100.
ANSWER: True
TOPIC: Production scheduling
10. Double-subscript notation for decision variables should be avoided unless
the number of decision variables exceeds nine.
ANSWER: False
TOPIC: Formulation notation
11. Using minutes as the unit of measurement on the left-hand side of a
constraint and using hours on the right-hand side is acceptable since both
are a measure of time.
ANSWER: False
TOPIC: General
12. Compared to the problems in the textbook, real-world problems generally
require more variables and constraints.
ANSWER: True
TOPIC: General
13. For the multi period production scheduling problem in the textbook, period n
- 1's ending inventory variable was also used as period n's beginning
inventory variable.
ANSWER: True
TOPIC: Production scheduling
14. A company makes two products, A and B. A sells for $100, and B sells for
$90. The variable production costs are $30 per unit for A and $25 for B. The
company's objective could be written as: MAX 190x - 55x .
1 2
ANSWER: False
TOPIC: Production scheduling
15. The primary limitation of linear programming's applicability is the
requirement that all decision variables be nonnegative.
ANSWER: False
TOPIC: General
16. A decision maker would be wise to not deviate from the optimal solution
found by an LP model because it is the best solution.
ANSWER: False
TOPIC: General Chapter 9 Linear Programming Applications 5
PROBLEMS
1. A&C Distributors is a company that represents many outdoor products
companies and schedules deliveries to discount stores, garden centers, and
hardware stores. Currently, scheduling needs to be done for two lawn
sprinklers, the Water Wave and Spring Shower models. Requirements for
shipment to a warehouse for a national chain of garden centers are shown
below.
Shippin Minimum Unit Cost Per Unit
Mont g Product Requireme to Ship Inventory
h Capacit nt Cost
y
Marc 8000 Water Wave 3000 .30 .06
h
Spring 1800 .25 .05
Shower
April 7000 Water Wave 4000 .40 .09
Spring 4000 .30 .06
Shower
May 6000 Water Wave 5000 .50 .12
Spring 2000 .35 .07
Shower
Let Sije the number of units of sprinkler i shipped in month j, where i = 1 or
2, and j = 1, 2, or 3. Let ijbe the number of sprinklers that are at the
warehouse at the end of a month, in excess of the minimum requirement.
a Write the portion of the objective function that minimizes shipping
costs.
b. An inventory cost is assessed against this ending inventory. Give the
portion of the objective function that represents inventory cost.
c. There will be three constraints that guarantee, for each month, that
the total number of sprinklers shipped will not exceed the shipping
capacity. Write these three constraints.
d. There are six constraints that work with inventory and the number of
units shipped, making sure that enough sprinklers are shipped to meet
the minimum requirements. Write these six constraints.
TOPIC: Production scheduling 6 Chapter 9Linear Programming Applications
2. An ad campaign for a new snack chip will be conducted in a limited
geographical area and can use TV time, radio time, and newspaper ads.
Information about each medium is shown below.
Medium Cost Per # Reached Exposure
Ad Quality
TV 500 10000 30
Radio 200 3000 40
Newspaper 400 5000 25
If the number of TV ads cannot exceed the number of radio ads by more than
4, and if the advertising budget is $10000, develop the model that will
maximize the number reached and achieve an exposure quality if at least
1000.
TOPIC: Media selection
3. Information on a prospective investment for Wells Financial Services is given
below.
Period
1 2 3 4
Loan Funds Available 3000 7000 4000 5000
Investment Income
(% of previous period’s 110% 112% 113%
investment)
Maximum Investment 4500 8000 6000 7500
Payroll Payment 100 120 150 100
In each period, funds available for investment come from two sources: loan
funds and income from the previous period's investment. Expenses, or cash
outflows, in each period must include repayment of the previous period's
loan plus 8.5% interest, and the current payroll payment. In addition, to end
the planning horizon, investment income from period 4 (at 110% of the
investment) must be sufficient to cover the loan plus interest from period 4.
The difference in these two quantities represents net income, and is to be
maximized. How much should be borrowed and how much should be
invested each period?
TOPIC: Financial planning
4. Tots Toys makes a plastic tricycle that is composed of three major
components: a handlebar-front wheel-pedal assembly, a seat and frame
unit, and rear wheels. The company has orders for 12,000 of these tricycles.
Current schedules yield the following information.
Cost to Cost to
Requireme
nts Chapter 9 Linear Programming Applications 7
Component Plastic Time Space Manufactu Purchas
re e
Front 3 10 2 8 12
Seat/Frame 4 6 2 6 9
Rear wheel .5 2 .1 1 3
(each)
Available 50000 16000 30000
0
The company obviously does not have the resources available to
manufacture everything needed for the completion of 12000 tricycles so has
gathered purchase information for each component. Develop a linear
programming model to tell the company how many of each component
should be manufactured and how many should be purchased in order to
provide 12000 fully completed tricycles at the minimum cost.
TOPIC: Make or buy
5. The Tots Toys Company is trying to schedule production of two very popular
toys for the next three months: a rocking horse and a scooter. Information
about both toys is given below.
Begin. Requir Require Productio Productio
Invty. ed d n n
Toy June 1 Plastic Time Cost Cost
Rocking 25 5 2 12 1
Horse
Scooter 55 4 3 14 1.2
Plastic Time Monthly Monthly
Demand Demand
Summer Availabl Availabl Horse Scooter
Schedule e e
June 3500 2100 220 450
July 5000 3000 350 700
August 4800 2500 600 520
Develop a model that would tell the company how many of each toy to
produce during each month. You are to minimize total cost. Inventory cost
will be levied on any items in inventory on June 30, July 31, or August 31
after demand for the month has been satisfied. Your model should make use
of the relationship
Beginning Inventory + Production - Demand = Ending Inventory
for each month. The company wants to end the summer with 150 rocking
horses and 60 scooters as beginning inventory for Sept. 1. Don't forget to
define your decision variables.
TOPIC: Production scheduling 8 Chapter 9Linear Programming Applications
6. Larkin Industries manufactures several lines of decorative and functional
metal items. The most recent order has been for 1200 door lock units for an
apartment complex developer. The sales and production departments must
work together to determine delivery schedules. Each lock unit consists of
three components: the knob and face plate, the actual lock itself, and a set
of two keys. Although the processes used in the manufacture of the three
components vary, there are three areas where the production manager is
concerned about the availability of resources. These three areas, their usage
by the three components, and their availability are detailed in the table.
Knob and Lock Key Available
R Pl (each)
e at
s e
o
u
r
c
e
Brass 12 5 1 15000 units
Alloy
18 20 10 36000
Machining minutes
Finishing 15 5 1 12000
minutes
A quick look at the amounts available confirms that Larkin does not have the
resources to fill this contract. A subcontractor, who can make an unlimited
number of each of the three components, quotes the prices below.
Component Subcontractor Larkin Cost
Cost
Knob and 10.00 6.00
Plate
Lock 9.00 4.00
Keys (set of 1.00 .50
2)
Develop a linear programming model that would tell Larkin how to fill the
order for 1200 lock sets at the minimum cost.
TOPIC: Make-or-buy
7. G and P Manufacturing would like to minimize the labor cost of producing
dishwasher motors for a major appliance manufacturer. Although two
models of motors exist, the finished models are indistinguishable from one
another; their cost difference is due to a different production sequence. The Chapter 9 Linear Programming Applications 9
time in hours required for each model in each production area is tabled here,
along with the labor cost.
Model 1 Model 2
Area A 15 3
Area B 4 10
Area C 4 8
Cost 80 65
Currently labor assignments provide for 10,000 hours in each of Areas A and
B and 18000 hours in Area C. If 2000 hours are available to be transferred
from area B to Area A, 3000 hours are available to be transferred from area C
to either Areas A or B, develop the linear programming model whose solution
would tell G&P how many of each model to produce and how to allocate the
workforce.
TOPIC: Workforce assignment
8. FarmFresh Foods manufactures a snack mix called TrailTime by blending
three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture.
Information about the three ingredients (per ounce) is shown below.
Volu Fat Calorie
Ingredient Cost
me Grams s
Dried Fruit .35 1/4 0 150
cup
3/8
Nut Mix .50 cup 10 400
Cereal Mix .20 1 1 50
cup
The company needs to develop a linear programming model whose solution
would tell them how many ounces of each mix to put into the TrailTime
blend. TrailTime is packaged in boxes that will hold between three and four
cups. The blend should contain no more than 1000 calories and no more
than 25 grams of fat. Dried fruit must be at least 20% of the volume of the
mixture, and nuts must be no more than 15% of the weight of the mixture.
Develop a model that meets these restrictions and minimizes the cost of the
blend.
TOPIC: Blending
9. The Meredith Ribbon Company produces paper and fabric decorative ribbon
which it sells to paper products companies and craft stores. The demand for
ribbon is seasonal. Information about projected demand and production for a
particular type of ribbon is given.
Demand Production Cost Per Production Capacity
(yards) Yard (yards) 10 Chapter 9 Linear Programming Applications
Quarter 10,000 .03 30,000
1
Quarter 18,000 .04 20,000
2
Quarter 16,000 .06 20,000
3
Quarter 30,000 .08 15,000
4
An inventory holding cost of $.005 is levied on every yard of ribbon carried
over from one quarter to the next.
a. Define the decision variables needed to model this problem.
b. The objective is to minimize total cost, the sum of production and
inventory holding cost. Give the objection function.
c. Write the production capacity constraints.
d. Write the constraints that balance inventory, production, and demand
for each quarter. Assume there is no beginning inventory in quarter 1.
e. To attempt to balance the production and avoid large changes in the
workforce, production in period 1 must be within 5000 yards of
production in period 2. Write this constraint.
TOPIC: Production scheduling
10. Island Water Sports is a business that provides rental equipment and
instruction for a variety of water sports in a resort town. On one particular
morning, a decision must be made of how many Wildlife Raft Trips and how
many Group Sailing Lessons should be scheduled. Each Wildlife Raft Trip
requires one captain and one crew person, and can accommodate six
passengers. The revenue per raft trip is $120. Ten rafts are available, and at
least 30 people are on the list for reservations this morning. Each Group
Sailing Lesson requires one captain and two crew people for instruction. Two
boats are needed for each group. Four students form each group. There are
12 sailboats available, and at least 20 people are on the list for sailing
instruction this morning. The revenue per group sailing lesson is $160. The
company has 12 captains and 18 crew available this morning. The company
would like to maximize the number of customers served while generating at
least $1800 in revenue and honoring all reservations.
TOPIC: Scheduling
11. Evans Enterprises has bought a prime parcel of beachfront property and
plans to build a luxury hotel. After meeting with the architectural team, the
Evans family has drawn up some information to make preliminary plans for
construction. Excluding the suites, which are not part of this decision, the
hotel will have four kinds of rooms: beachfront non-smoking, beachfront
smoking, lagoon view non-smoking, and lagoon view smoking. In order to
decide how many of each of the four kinds of rooms to plan for, the Evans
family will consider the following information. Chapter 9 Linear Programming Applications 11
a. After adjusting for expected occupancy, the average nightly revenue
for a beachfront non-smoking room is $175. The average nightly
revenue for a lagoon view non-smoking room is $130. Smokers will be
charged an extra $15.
b. Construction costs vary. The cost estimate for a lagoon view room is
$12,000 and for a beachfront room is $15,000. Air purifying systems
and additional smoke detectors and sprinklers ad $3000 to the cost of
any smoking room. Evans Enterprises has raised $6.3 million in
construction guarantees for this portion of the building.
c. There will be at least 100 but no more than 180 beachfront rooms.

More
Less
Unlock Document

Related notes for ADMS 3330

Only pages 1,2,3,4 are available for preview. Some parts have been intentionally blurred.

Unlock DocumentJoin OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.