Problem 1 (25 pts) : Network Flow (similar to iPad transportation

the example we did in class)

(Adapted from Winston and Albright)

Supplying Power at Northeast Electric: Northeast Electric has three electric power plants that supply the

power needs of four cities. Each power plant can supply the amounts shown in the table below (in millions

of kilowatt-hours of electricity):

Supply

Plant 1

35

Plant 2

50

Plant 3

40

The power demand (again in millions of kwh) in each city is given in the following table:

Demand

State College

45

Bellefonte

20

Altoona

30

Lock Haven

30

Finally, the cost (in dollars) of sending a million kwh from each plant to each city is given in the following

table:

State College

Bellefonte

Altoona

Lock Haven

Plant 1

8

6

10

9

Plant 2

9

12

13

7

Plant 3

12

9

16

5

Northeast Electric wants to find the lowest-cost method for meeting the demand of the four cities.

Answer the following questions:

a.

How many decision variables do you have here? How many constraints?

b. Build a network flow model for Northeast and solve it using Solver.

c.

Identify binding and nonbinding constraints in your solution.

d. Pick any of the constraints in your model. What is the shadow price for this constraint? What

does this shadow price mean for your model?

e. If you had one extra million of kwh of electricity available, which plant would you want to

allocate this amount to? Explain why.