Any help would be great. The direction for the solver are attached

1)

Tri-State is trying to determine the optimal direct-shipping route from Chicago to Cleveland that minimizes the total traveling distance. To formulate the problem, Tri-State uses a binary decision variable defined as follows: X_i,j = 1 if the link between node i and j is selected; 0 if the link not selected.

Assume that each link in the diagram is a 2 directional arrow. In order to find the optimal solution and value of Z, how many different decision variables need to be present in the objective function?

2)

QUESTION 2

1. Tri-State is trying to determine the optimal direct-shipping route from Chicago to Cleveland that minimizes the total traveling distance. To formulate the problem, Tri-State uses a binary decision variable defined as follows: X_i,j = 1 if the link between node i and j is selected; 0 if the link not selected.

   How many constraints should be present in the LP model for this problem?

0.5 points

QUESTION 5

1. Assume now, that for the Cleveland shipment, the Tri-State wishes to drop by Cincinnati along the delivery. In particular, it must drop by at Cincinnati and then complete the shipment at its final destination, Cleveland.

   Select all of the following that are necessary constraints to add in order to model this situation:

   		Both X2,6 + X4,6 + X7,6 = 1 and X6,2 + X6,4 + X6,7 = 1 could be used(assume there is no conservation constraint in the model).
   		Only X6,2 + X6,4 + X6,7 = 1 is necessary (assume there is no conservation constraint in the model).
   		Only X2,6 + X4,6 + X7,6 = 1 is necessary (assume there is no conservation constraint in the model).
   		If X2,6 + X4,6 + X7,6 = X6,2 + X6,4 + X6,7 is in the model, then only one of the constraints in choice A is necessary, but not both

QUESTION 7

1. Given the new modification (i.e. that the shipment must be transported through Cincinnati), what is the new path the truck will take when transporting paint from Chicago to Cleveland?

Question 8

Assume now, that in addition to stopping by Cincinnati along the delivery, the company has learned of miles of construction taking place on the route between Chicago and Indianapolis, and therefore wants to make sure not to take that route. The company has also learned that there is a rush order that must be delivered to Green Bay first before reaching Cleveland. Given these modification, what is the new minimum number of miles through this network, from Chicago to Cleveland?

9)Given the new modifications you placed in your model in the previous question, what is the new path the truck will take when transporting paint from Chicago to Cleveland?

10)What is the value the objective function for this transshipment problem (i.e. the minimized transportation cost)?

5 The Tri-State shipping company transports paint from Chicago, IL (node 1) to six cities in the Midwest. The cities that the company 3 450miles ships to include: 200miles 300miles Node 2: Indianapolis, IN 215 miles 160miles Node 3: Green Bay, WI 100miles Node 4: South Band, IN 250iles 400miles Node 5: Ann Arbor, MI 180miles 225miles Node 6: Cincinnati, OH Node 7: Cleveland, OH 120miles Tri-State is trying to determine the optimal direct-shipping route from Chicago (1) to Cleveland (7) that minimizes the total traveling distance. Assume that there can be 2-way transportation between each connection of nodes (i.e. for example, there is a bi-directional arrow between nodes 1 & 2). To formulate the problem, Tri-State uses a binary decision variable defined as follows: Xij = 1 if the link between node i and j is selected; O if the link not selected. (a) Create the linear programming model in Excel Solver to find the optimal distance and shipping route (Answer questions 1-4 on Compass using this output). (b) Assume now, that for the Cleveland shipment, the Tri-State wishes to drop by Cincinnati along the delivery. In particular, it must drop by at Cincinnati and then complete the shipment at its final destination, Cleveland. Add the new constraints to your model and find the optimal solution and value of Z for this modification (Answer questions 5-7 on Compass using this output) (c) Assume now, that in addition to stopping by Cincinnati along the delivery, the company has learned of miles of construction taking place on the route between Chicago and Indianapolis, and therefore wants to make sure not to take that route. The company has also learned that there is a rush order that must be delivered to Green Bay first before reaching Cleveland. Add the new constraints to your model and find the optimal solution and value of Z for this modification (Answer questions 8-9 on Compass using this output)