One power system has 3 electric power plants that supply the needs of 3 cities

3) One power system has 3 electric power plants that supply the needs of 3 cities.

The capacity of each power plant was given in the Table below (in MW). The power

demands in these cities are as follows (in MW): city1—45; city 2—20; city 3—30; The costs

of sending 1 MW of electricity from plant to city are given:

From To Supply (MW) City 1 City 2 City 3

Plant 1 5 15 17 35

Plant 2 16 21 20 20

Plant 3 9 8 10 40

Demand (MW) 45 20 30

Formulate a transportation problem to minimize the cost of supplying the power

demands to 3 cities. (Defining variables, objective function, constraints) (2đ)

4) One power system that has 3 electric power plants supplying the needs of 4 cities. The

availability of each power plant: 20, 30, 45 MW. The cost for electricity transportation from

power plants to 4 cities are:

C11 = 12 C12 = 5 C13 = 16 C14 = 18

C21 = 10 C22 = 9 C23 = 20 C24 = 14

C31 = 8 C32 = 11 C33 = 13 C34 = 17

The demands of 4 cities are: 20, 25, 15, 35 MW.

Find the power transported from each plant to each city in order to minimize the total

cost. (3đ)