Final Exam Statement: MGS511 - Fall of 2016 (48% Final Grade) I) For the assignment problem described in the table below (costs/hour in the table): 12 PTS Task Consult 1 2 3 A 9 12 11 B 5 6 6 C 4 3 5 D 2 5 7 a) Show both the network and the linear programming formulation (for Lingo) b) Solve the problem using Lingo SW and interpret the solution results. c) Solve again, assuming Consultant 1 cannot work on Task B, and taking out Task C II) Consider the following shortest-route problem involving 6 cities with the distances given. (1) Draw the network for this problem. (2) Formulate and (3) Solve the LP (in Lingo) for finding the shortest distance from City 1 to City 6. 12 PTS Path 1 to 2 1 to 3 2 to 4 2 to 5 3 to 4 3 to 5 4 to 6 5 to 6 Distance 3 2 4 5 3 7 6 2 III) For the Network below, (1) obtain the Maximum Flow equations: 14 PTS. 3 2 2 1 3 1 4 1 3 4 2 4 5 6 2 3 Then, (2) solve the problem using LINGO and (3) discuss the solution. Fill the blanks below with the solution information of the above problem: Objective Function: Node equilibrium equations: Node 1: Node 2: Node 3: Node 4: Node 5: Node 6: Arc Capacitation Constraints defined by: Node 1: Node 2: Node 3: Node 4: Node 5: Non-negativity constraints: IV) Interpret the following output, for a Trans-shipment problem: 10 PTS Objective Function = 1045000.000 VARIABLE X15 X18 X26 X29 X37 X310 X411 X59 X510 X610 X611 X711 VALUE 150.000 300.000 0.000 500.000 0.000 500.000 400.000 0.000 150.000 0.000 0.000 0.000 REDUCED COST 0.000 0.000 100.000 0.000 250.000 0.000 0.000 0.000 0.000 0.000 150.000 0.000 1. What is the value of the solution? 2. How much (total) production will be transferred out of Node 1? 3. Into which Nodes, and how much production to each node? 4. Why is the Reduced Cost of X15 Zero? 5. Why is the Reduced Cost of X26 Greater than Zero? 6. Why are the Value and Reduced cost of X711 both zero