Please clearly explain decision variable and binary variables note (there is one available solution but it is not sufficient,)

mathematical model like

min .....

s.t

constraint 1

constraint 2

constraint 3

sign constraints...

Plants Warehouses Markets CD 1) (30 points) The SCM company plans to open a new single plant among four potential location options as can be seen in figure presented right. Five warehouses act as intermediaries between plants and markets each of which has a known demand that needs to be satisfied. It is assumed that only direct deliveries are possible between plants and warehouses, and between warehouses and markets. The demands of each market are as follows: 100, 200, 300, 400 and 500 consecutively. The rest of the data are presented in Tables 1 to 3. Question is to develop a mathematical model to identify plant locations and quantities shipped that minimize Figure 1 Representation of the supply chain network the total fixed and variable costs. (Define parameters and decision variables explicitly.) Table 1 Potential plant capacities and corresponding fixed costs in TL Potential plant Capacity Fixed cost of opening potential plant 10000 1700 20000 1600 1 2 3 1800 1900 30000 40000 4 Table 2 Cost of shipping one unit from potential plant p to warehouse w in TL 135 115 145 135 5 90 80 70 150 Warehouses 1 2 3 Potential Plant 1 100 105 100 Potential Plant 2 105 115 105 Potential Plant 3 110 125 120 Potential Plant 4 115 135 115 Table 3 Cost of shipping one unit from warehouse w to market m in TL Markets 1 2 3 Warehouse 1 60 105 100 Warehouse 2 105 115 165 Warehouse 3 70 125 120 Warehouse 4 115 155 145 Warehouse 5 105 115 105 4 135 125 145 175 115 5 60 90 75 150 180