1. Find the optimal solution.

2.Find the minimum total transport cost.

3.Consider the unit transport cost from Lyon to Marseille. What is the highest cost it can increase to without changing the optimal solution?

4.If Bordeaux starts charging inventory fee of 0.1 Euros for every unit they receive from Versailles, would the optimal transport scheme be affected? Why?

a.The optimal transport scheme would change, because if Bordeaux starts charging inventory fees, the company would not send as many units to Bordeaux to lower total cost.

b.The optimal transport scheme would change because introducing new (inventory) costs changes the entire LP problem.

c.The optimal transport scheme would not change because the inventory cost is very small.

d.The optimal transport scheme would not change because the inventory cost induces an increase in the cost of sending units from Versailles to Bordeaux, but the increase is not large enough to cause the optimal transport scheme to change.

e.There is not enough information to decide.

5.If the demands of the three retailers are each decreased by 250 units, what is the total percentage change? Find the new minimum transport cost.

A French company has two plants at Versailles and Rennes producing certain food product at weekly rates of 3000 units and 4500 units respectively. The units are transported to one of the two warehouses at Bordeaux and Lyon, and then to retailers at Toulouse, Marseille and Montpellier. The unit transport costs (in Euros) and demands of the retailers are shown below. Bordeaux (node 3) Lyon (node 4) Versailles (node 1) 6.4 6.6 Rennes (node 2) 6.2 6.5 Toulouse (node 5) demand = 3500 Marseille (node 6) Montpellier (node 7) demand = 2000 demand = 1800 Bordeaux 3.2 3.5 4.6 Lyon 3.2 3 4.5 The objective is to meet the demands at the lowest total cost. Let Xij be the number of units to be transported from node i to node j. Solve the LP problem using Excel and answer the following questions