A concrete company transports concrete from three plants, 1, 2 and 3, to three construction sites, A, B and C. The plants can supply the following quantity of concrete (in tons) per week: Plant Supply(Capacity)
1 300
2 300
3 100

The requirements of the sites, in number of tons per week, are:

Construction site Demand(requirment)
A 200
B 200
C 300

The cost of transporting I ton Of concrete from each plant to each site is shown in the table below (in dollars per ton).

From A B C
1 4 3 6
2 7 5 9
3 4 5 5

How much concrete should the company ship from each plant to each construction site to fill the demand while minimizing the transportation cost?
a. List and explain carefully what the decision variables are?
b. Write out the objective function.
c. Write out the constraints.