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• tehpohkee

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The Interstate Truck Rental firm has accumulated extra trucks at three of its truck leasing outlets, as shown in following table. Leasing Outlet

Extra Trucks

1.

Atlanta

70

2.

St. Louis

115

3.

Greensboro

60

Total

245

The firm also has four outlets with shortages of rental trucks, as follows.

Leasing Outlet

Trucks Shortage

A.

New Orleans

80

B.

Cincinnati

50

C.

Louisville

90

D.

Pittsburgh

25

Total

245

The firm wants to transkr trucks from those outlets with extras to those with shortages at the minimum total cost The following costs of transporting these trucks from city to city have been determined. To From A

B

C

D

1

$ 70

80

45

90

2

120

40

30

75

3

110

60

70

80

a.

Find the initial solution using the minimum cell cost method.

b.

Solve using the stepping-stone method.

2. Steel mills in three cities produce the following amounts of steel. Location

Weekly Production (tons)

A.

Bethlehem

150

B.

Birmingham

210

C.

Gary

320 680

These mills supply steel to four cities where manufacturing plants have the following demand. Location

Weekly Demand (tons)

1.

Detroit

130

2.

St. Louis

70

3.

Chicago

180

4.

Norfolk

240 620

Shipping costs per ton of steel are as follows. To From 1

2

3

4

A

$14

9

16

18

B

11

8

7

16

C

16

12

10

22

Because of a truckers' strike, shipments are at present prohibited from Birmingham to Chicago. a. Set up a transportation tableau for this problem and determine the initial solution. Identify the method used to find the initial solution. b. Solve this problem using MODI. c. Are there multiple optimal solutions? Explain. If so, identify them. d. Formulate this problem as a general linear programming model. e. What would be the effect on the optimal solution of a reduction in production capacity at the Gary mill from 320 tons to 290 tons per week?