Ashwane150 take note: The two set of questions require solution using the answer sheet provided. ALL QUESTIONS MUST BE ANSWERED.

1. transportaTon problem
From
±o (cost)
1
2
3
A
$6
$5
$5
B
11
8
9
C
4
10
7
DV
From
±o
Supply
Note: Blue cells are your decision variables
1
2
3
Constraint
A
0.00
100.00
50.00
150
<=
150
B
0.00
0.00
0.00
0
<=
85
C
70.00
0.00
30.00
100
<=
125
Constraint
70.00
100.00
80.00
=
=
=
Demand
70
100
80
ObjecTve Minimize Cost
$1,240.00

s

Cab Company Scheduling
let Di = # of drivers who start their 8 hour shiF in period I (I = 1,2,3,4,5,6)
period 1
12:00:00 AM--4:00am
period 4
12 noon -- 4:00pm
period 2
4:00am -- 8:00am
period 5
4:00pm -- 8:00pm
period 3
8:00am -- 12 noon
period 6
8:00pm -- midnight
period 1
period 2
period 3
period 4
period 5
period 6
average fare/ driver
80
500
420
300
270
210
# of drivers in each period
>=
>=
>=
>=
>=
>=
minimum # of drivers
10
12
20
25
32
18
DV
D1
D2
D3
D4
D5
D6
# of drivers/period
ObjecTve funcTon

Denim Jeans
CD Player
Compact discs
proft
90
150
30
weight
2
3
1
Denim Jeans
CD Player
Compact discs
DV
Constraint
<=
5
ObjecTve FuncTon

MAT540 Homework
Week 10
Page 1 of 2
MAT540
Week 10 Homework
Chapter 6
1.
Consider the following transportation problem:
From
To (Cost)
Supply
1
2
3
A
6
5
5
150
B
11
8
9
85
C
4
10
7
125
Demand
70
100
80
Formulate this problem as a linear programming model and solve it by the using the computer.
2.
Consider the following transportation problem:
From
To (Cost)
Supply
1
2
3
A
8
14
8
120
B
6
17
7
80
C
9
24
10
150
Demand
110
140
100
Solve it by using the computer.
3.
World foods, Inc. imports food products such as meats, cheeses, and pastries to the United States
from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports deliver the
products to Norfolk, New York and Savannah, where they are stored in company warehouses
before being shipped to distribution centers in Dallas, St. Louis and Chicago. The products are then
distributed to specialty foods stores and sold through catalogs. The shipping costs ($/1,000 lb.) from
the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports are
provided in the following table:

MAT540 Homework
Week 10
Page 2 of 2
From
To (Cost)
Supply
4.
Norfolk
5.
New York
6.
Savannah
1.
Hamburg
320
280
555
75
2.
Marseilles
410
470
365
85
3.
Liverpool
550
355
525
40
The transportation costs ($/1000 lb.) from each U.S. city of the three distribution centers and the
demands (1000 lb.) at the distribution centers are as follows:
Warehouse
Distribution Center
7.
Dallas
8.
St. Louis
9.
Chicago
4.
Norfolk
80
78
85
5.
New York
100
120
95
6.
Savannah
65
75
90
Demand
85
70
65
Determine the optimal shipments between the European ports and the warehouses and the
distribution centers to minimize total transportation costs.
4.
The Omega Pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales
regions. Given their various previous contacts, the sales persons are able to cover the regions in
different amounts of time. The amount of time (days) required by each salesperson to cover each
city is shown in the following table:
Salesperson
Region (days)
A
B
C
D
E
1
20
10
12
10
22
2
14
10
18
11
15
3
12
13
19
11
14
4
16
12
14
22
16
5
12
15
19
26
23
Which salesperson should be assigned to each region to minimize total time? Identify the optimal
assignments and compute total minimum time.

MAT540 Homework
Week 9
Page 1 of 3
MAT540
Week 9 Homework
Chapter 5
1.
Rowntown Cab Company has 70 drivers that it must schedule in three 8-hour shifts. However, the
demand for cabs in the metropolitan area varies dramatically according to time of the day. The
slowest period is between midnight and 4:00 A.M. the dispatcher receives few calls, and the calls
that are received have the smallest fares of the day. Very few people are going to the airport at that
time of the night or taking other long distance trips. It is estimated that a driver will average $80 in
fares during that period. The largest fares result from the airport runs in the morning. Thus, the
drivers who sart their shift during the period from 4:00 A.M. to 8:00 A.M. average $500 in total
fares, and drivers who start at 8:00 A.M. average $420. Drivers who start at noon average $300, and
drivers who start at 4:00 P.M. average $270. Drivers who start at the beginning of the 8:00 P.M. to
midnight period earn an average of $210 in fares during their 8-hour shift.
To retain customers and acquire new ones, Rowntown must maintain a high customer service level.
To do so, it has determined the minimum number of drivers it needs working
during every 4-hour
time segment- 10 from midnight to 4:00 A.M. 12 from 4:00 to 8:00 A.M. 20 from 8:00 A.M. to
noon, 25 from noon to 4:00 P.M., 32 from 4:00 to 8:00 P.M., and 18 from 8:00 P.M. to midnight.
a.
Formulate and solve an integer programming model to help Rowntown Cab schedule its
drivers.
b.
If Rowntown has a maximum of only 15 drivers who will work the late shift from
midnight to 8:00 A.M., reformulate the model to reflect this complication and solve it
c.
All the drivers like to work the day shift from 8:00 A.M. to 4:00 P.M., so the company
has decided to limit the number of drivers who work this 8-hour shift to 20. Reformulate
the model in (b) to reflect this restriction and solve it.
2.
Juan Hernandez, a Cuban athlete who visits the United States and Europe frequently, is allowed to
return with a limited number of consumer items not generally available in Cuba. The items, which
are carried in a duffel bag, cannot exceed a weight of 5 pounds. Once Juan is in Cuba, he sells the
items at highly inflated prices. The weight and profit (in U.S. dollars) of each item are as follows:

MAT540 Homework
Week 9
Page 2 of 3
Item
Weight (lb.)
Profit
Denim jeans
2
$90
CD players
3
150
Compact discs
1
30
Juan wants to determine the combination of items he should pack in his duffel bag to maximize
his profit. This problem is an example of a type of integer programming problem known as a
“knapsack” problem. Formulate and solve the problem.
3.
The Texas Consolidated Electronics Company is contemplating a research and development
program encompassing eight research projects. The company is constrained from embarking on all
projects by the number of available management scientists (40) and the budget available for R&D
projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice
versa). Following are the resources requirement and the estimated profit for each project.
Project
Expense
($1,000s)
Management
Scientists required
Estimated Profit
(1,000,000s)
1
50
6
0.30
2
105
8
0.85
3
56
9
0.20
4
45
3
0.15
5
90
7
0.50
6
80
5
0.45
7
78
8
0.55
8
60
5
0.40
Formulate the integer programming model for this problem and solve it using the computer.
4.
Corsouth Mortgage Associates is a large home mortgage firm in the southeast. It has a poll of
permanent and temporary computer operators who process mortgage accounts, including posting
payments and updating escrow accounts for insurance and taxes. A permanent operator can process
220 accounts per day, and a temporary operator can process 140 accounts per day. On average, the
firm must process and update at least 6,300 accounts daily. The company has 32 computer

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