Case Study 1: Consider the following Excel sheet for a solved linear programming model of a maximal flow problem that represents a road network, and then answer the questions below: A B C D E F GHIJK | L M N OP Q R Variables X12 x21 x13 x31 x23 x32 x24 x42 x25 x52 x35 x53 x45 x54 x46 x64 x56 x65 x61 obj. fnc. nodel node 2 -1 -1 1 1 -1 node 3 1 -1 node 4 1 1 -1 node 5 1 -1 -1 node 6 1 41 x12 1 x21 1 x13 x31 x23 x32 x24 x42 x25 x52 x35 1 1 1 x53 x45 x54 x45 x64 x56 x65 STUVW 16 10 = 0 = 0 => 0 => 0 = -10= 44 0 = 2 23 45 0 => 0 22 0 = JOAOOWONOUWOO 03 0 = 0 = 01 44 0 => 22 1 0 => Var value Required: 1. Draw the network representation for this problem. 2. Formulate the objective function for this model. 3. Formulate the non-negativity constraint. 0 o 2 0 6 4. State two other types of constraints in the linear programming model for this maximal flow network and write two constraints only under each type. 5. Determine the following: The maximal flow of cars. The number of fully utilized routes and mention them. Two used arcs but below their capacity, specifying the remaining capacity of each. The number of one war arcs and the number of two ways arcs.