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
Plant 1
Plant 2
Plant 3
Demand (MW)

City 1
5
16
9
45

To
City 2
15
21
8
20

City 3
17
20
10
30

Supply (MW)

35
20
40

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
C21 = 10
C31 = 8

C12 = 5
C22 = 9
C32 = 11

C13 = 16
C23 = 20
C33 = 13

C14 = 18
C24 = 14
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)