Answer to Question #269897 in Operations Research for Kram

Question

Coal is mined and processed at the following four mines in Kentucky, West Virginia, and Virginia:

Location Capacity (tons)

A. Cabin Creek 90

B. Surry 50

C. Old Fort 80

D. McCoy 60 ____

280

These mines supply the following amount of coal to utility power plants in three cities:

Plant Demand (tons)

1. Richmond 120

2. Winston-Salem 100

3. Durham 110 ____

330

The railroad shipping costs ($1,000s) per ton of coal are shown in the following table. Because of

railroad construction, shipments are now prohibited from Cabin Creek to Richmond:

To

From 1 23

A $ 7 $10 $ 5

B 12 9 4

C 7 3 11

D 9 57

a. Set up the transportation tableau for this problem, determine the initial solution using

VAM, and compute total cost.

b. Solve using MODI.

c. Are there multiple optimal solutions? Explain. If there are alternative solutions, identify them.

d. Formulate this problem as a linear programming model.

Answer 1

a)

b)

c)The alternate solution is available with unoccupied cell C1:d$_{31}$ =0 but with the same optimal value

d)Min $7x_{11}+10x_{12}+5x_{13}+12x_{21}+9x_{22}+4x_{22}+7x_{31}+3x_{32}+11x_{33}+9x_{41}+5x_{42}+7x_{43}$