2. Factory Fi produces up to 5 units of a chemical per week at a cost of 2 per unit. Factory F2 produces up to 3 units of the same chemical per week at a cost of 3 per unit. The factories supply two shops, S, and S2. Shop S, requires 4 units per week. Shop S2 requires 4 units per week. The cost of transporting the chemical from the factories to the shops is given by Si S2 F 3 4 F22 6 (a) Describe how to construct an incremental network in Ford-Fulkerson's algorithm if one wants to find a flow through the network that minimizes the overall cost. [6 Marks) (b) Construct a flow network for the factory-shop system described above that clearly shows the capacities and costs. [6 Marks) (c) Use the Ford-Fulkerson algorithm to find a flow through the network found in (b) that minimizes the overall cost. [8 Marks 2. Factory Fi produces up to 5 units of a chemical per week at a cost of 2 per unit. Factory F2 produces up to 3 units of the same chemical per week at a cost of 3 per unit. The factories supply two shops, S, and S2. Shop S, requires 4 units per week. Shop S2 requires 4 units per week. The cost of transporting the chemical from the factories to the shops is given by Si S2 F 3 4 F22 6 (a) Describe how to construct an incremental network in Ford-Fulkerson's algorithm if one wants to find a flow through the network that minimizes the overall cost. [6 Marks) (b) Construct a flow network for the factory-shop system described above that clearly shows the capacities and costs. [6 Marks) (c) Use the Ford-Fulkerson algorithm to find a flow through the network found in (b) that minimizes the overall cost. [8 Marks