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日期：2018-06-04 02:32

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41. It is anticipated that steel production at a new plant in

Bethlehem, Pennsylvania, will generate approximately

50,000 gallons of raw sewage per hour that must be

treated at a local treatment facility. The plant plans to

use excess capacity on existing pipes. Will the existing

system of pipes between pumping stations be sufficient

42. The Wichita State University (WSU) baseball team is

preparing for the upcoming college world series. It has

two games left in the regular season, followed by at least

two games in the double elimination World Series

tournament. WSU has already played three of the four

teams—Texas (UT), Arizona State (ASU), and Florida

State (FSU)—and is very familiar with its other

opponent, California State University, Fullerton

(CSUF).

WSU has four starting pitchers and will start a

different one against each team. Based on past

performance, the WSU coach has compiled an

effectiveness statistic for each pitcher based on the

pitcher’s and the opponent team’s strengths and

weaknesses. He has used these statistics throughout the

year, which may account for his successful 45–12

won–lost record. The effectiveness statistics for these

opponents are as follows.

Effectiveness Factors

UT ASU FSU CSUF

Clyde Rollins 62 65 80 50

Carlos Pascual 76 70 82 55

Sid Thompson 75 40 77 57

Ted Quillici 45 48 50 36

a. Based on these factors, which pitcher should WSU

start against each team to maximize the total overall

effectiveness rating?

b. Suppose the WSU coach will let a pitcher start up to

two games. Modify the problem and solve first as an

assignment problem and then as a transportation

problem.

c. Use the transportation model format to determine

the starting pitchers if the WSU coach will allow a

pitcher to start as many as three games.

43. During the early 1970s, the political scandal Watergate

shook the United States and toppled a presidency. While

there were many aspects to the episode (robbery,

enemies lists, abuse of power, cover-ups, etc.), a key

component was the “laundering” of funds from big

money contributors to campaign coffers. This practice

consists of channeling a large “gift” of money through

various banks and individuals so that its source cannot be

traced. Unfortunately, such activities continue today as

evidenced by congressional investigations beginning in

1997.

Suppose millionaire I. S. Halverson has $5000 (in

reality, he would probably have 10 or 100 times this

amount) that he would like to donate “anonymously” to

the Independent National Party (INP). He might first

split the money up in smaller units and deposit the

money in several bank accounts spread throughout the

world. Money from these accounts could be mixed or

further divided and sent to other accounts or individuals,

who, in turn, would do the same, until several checks for

$1000 or less eventually arrive at party headquarters.

To avert suspicion, a limit has been placed on the

amount of each transaction between intermediaries.

These limits are given in the network at the top of the

next page depicting I. S. Halverson, the intermediaries,

and the INP. Given these limitations, how much of the

$5000 can I. S. Halverson launder to the INP?

(Note: The federal government employs management

scientists who also use such models to help determine

transaction limits that should be monitored.)

to support this operation, or will additional piping

capacity be required? (The numbers give the maximum

number of thousands of gallons per hour possible through

each pipe.) Sewage can flow in either direction between

Stations 1 and 2 and Stations 4 and 5.

Additional Problems/Cases CD-465

Chapter 4 Extra Problems/Cases

Steel Plant Treatment

Facility Station 3

Station 1 Station 4

Station 2 Station 5

35 5 55

25 15

10

10

45

35

20 10

80

Problem 41

44. Luxor Motorhomes has two plants, one in Riverside,

California, and the other in Des Moines, Iowa. Each

plant can produce three different models: the Grand

Cruiser, the Traveler, and the Weekender. Labor time

at the Riverside plant limits production to 600 models

per month, while the Des Moines plant can produce up

to 1000 models per month. The manufacturing costs and

monthly production capacities for each model vary,

depending on the plant. These costs are summarized in

the following table.

Manufacturing Costs and Maximum Monthly

Production Levels

Riverside Des Moines

Manufacturing Cost

Grand Cruiser $53,000 $50,000

Traveler $29,000 $27,000

Weekender $18,000 $17,000

Maximum Monthly Production

Grand Cruiser 200 400

Traveler 500 500

Weekender 600 900

Once the units are manufactured, they are shipped to

central distribution locations in Florida, Texas, and

California, where they are ultimately purchased by

retailers. The demand for motorhomes at the

distribution locations for this month’s production is as

follows.

Demand for Motorhomes

Florida Texas California

Grand Cruiser 100 50 150

Traveler 200 100 300

Weekender 225 175 250

The transportation costs for shipping a motorhome

from a plant to a distribution center are independent of

the model. These are given in the following table.

Motorhome Shipping Costs

Florida Texas California

Des Moines $1000 $800 $1200

Riverside $2000 $700 $ 300

Formulate this problem as a capacitated

transshipment problem and solve for the optimal

production and distribution of motorhomes during this

month.

(Hint: Define a set of nodes for the plants, a set for the

models, and a set for the models at the distribution

locations.)

45. The Texas Education Association wishes to hold its

annual meeting in one of three cities: Dallas, Austin, or

Abilene. Representatives from 21 different school

districts will attend, including representatives from the

three possible host cities. The driving distances in miles

are given in the network for problem 45 on the next

page. Assume that each attendee will drive the shortest

route from his or her city to the meeting site.

a. Which site should be selected if the goal is to

minimize the maximum driving distance of any

attendee?

b. Which site should be selected if the goal is to

minimize the average driving distance of all the

attendees?

46. The small rural town of Campton has only one

elementary school. Beginning early every morning, a

school bus leaves the school, picks up children at four

stops, and returns to the school. The table for problem

46 gives the distances between the stops.

Problem 46 Miles Between Pickup Points

Willow General Old

Crossroad Creek Store Highway

School 6 29 24 10

Crossroad 19 21 20

Willow Creek 5 27

General Store 16

CD-466 Chapter 4 Extra Problems/Cases

6 1

2

2000

2000

250

1500

1000

1000

1000

1000

1000

2000

100

300

200

400

3

4

5

INP

I.S. Halverson

Numbers on the arcs represent the maximum amount that can be laundered in either direction.

Problem 43

49. Topless City is a small chain of car dealerships that

sells vintage convertibles throughout the Southern

United States. It is owned and managed by Brandon

and Kyle Winslow. Each month Brandon and Kyle

attend two car auctions, at which they purchase

convertibles: one in Atlanta, the other in Miami. The

cars are then shipped to one of three locations: Jackson,

Mississippi, Birmingham, Alabama, or Orlando,

Florida. There, the cars are refurbished, repainted,

safety inspected, and sold at the Topless City

dealership in that city.

In August, Brandon found 20 cars at the Atlanta

auction, and Kyle found 50 cars at the Miami auction

which met the needs of the company. Only 15 cars can

be worked on at each city during the month, however.

Another auction is coming up in September; thus, only

45 cars are to be purchased in August.

Topless City wishes to minimize its costs of

transporting the cars to the refurbishing locations. The

cost to transport cars between cities is shown in the table

for problem 49.

Problem 49

Jackson Birmingham Orlando

Atlanta $200 $100 $175

Miami $250 $200 $125

a. Give a linear programming formulation for this

problem.

b. Formulate the problem as a transportation problem

and solve.

c. Do the assumptions of the transportation model

appear to be valid for this problem? Comment.

50. Consider the situation faced by Topless City in problem

49. For some time now, Brandon and Kyle have been

considering converting their facilities in these three

cities to sales lots only and performing all refurbishing

operations in other cities. If they do so, they can actually

use all 70 cars: 15 in Jackson, 25 in Birmingham, and 30

in Orlando.

One plan under consideration is to contract out the

painting to shops in Tuscaloosa, Alabama, and

Columbus, Georgia, and then transport the cars for

mechanical work to shops in Montgomery, Alabama, and

Gainesville, Florida, before delivery to a Topless City

location. Alternatively, a full-service operation in

Jacksonville could handle both the painting and

mechanical work.

a. Given the tables for problem 50, which reflect the

average unit transportation costs per vehicle between

locations, formulate the problem as a transshipment

problem and solve for the optimal shipping patterns.

How many cars are painted and fixed mechanically in

each location? Explain.

Tables for Problem 50

To

Tuscaloosa Columbus Jacksonville

From

Atlanta $150 $ 75 $150

Miami $200 $175 $125

To

Montgomery Gainesville

From

Tuscaloosa $50 $100

Columbus $50 $ 75

CD-468 Chapter 4 Extra Problems/Cases

23,000

Buy 2-Year-Old Car

6000

Keep

Buy New Car

31,760

3000

Keep

16,000

Buy New Car

42,000

Buy New Car 1 1

2

4

3

Purchase +

Operating Cost

Year 1 Year 2 Year 3 Year 4 Year 5

Purchase +

Operating CostTrade-in

Age at

Beginning of

Year 2

Operating

Cost

START

Problem 48

To

Jackson Birmingham Orlando

From

Montgomery $130 $ 70 $110

Gainesville $150 $135 $ 45

Jacksonville $180 $130 $ 60

b. After painting and refurbishing the vehicles and

deducting other expenses (sales personnel, utilities,

etc.), the average gross profit is $x per car. Based on

the August auction figures, what breakeven value of x

would justify implementing the new plan of buying

and selling all 70 cars, rather than maintaining the

current policy of purchasing 45 cars and doing all the

work at Topless City locations?

c. Solve for the shortest path (in terms of cost) from

Atlanta to the Topless City locations; solve for the

shortest path from Miami to the Topless City

locations.

d. Use the results of part (c) to convert the

transshipment problem to a transportation problem.

Solve and show that the solutions are equivalent to

those found in part a.

Additional Problems/Cases CD-469