PLEASE help me with this question!! I have been working on it for 4 hours and I still don't know what goes in the blanks. PLEASE tell me specifically what goes in each blank. Thank you!

Consider the following transshipment network for finding the shortest route from node 1 to node 7.

A

A network diagram between seven parties, distributed across four columns, is shown. The left-most column contains node 1. The second column contains nodes 2, 3, and 4. The third column contains nodes 5 and 6. The right-most column contains node 7. Arrows are shown between various locations. The following list contains the numbers placed on the graph.

• 12: 7
• 13: 9
• 14: 18

• 23: 3
• 25: 5

• 32: 3
• 35: 4

• 46: 3

• 52: 5
• 53: 4
• 56: 2
• 57: 6

• 65: 2
• 67: 3

• 7: no departing arrows

(a)

Formulate a linear programming model of the problem. (Express your answers using x_ij, where each x_ij is either 0 or 1 for the arc from node i to node j.)

Min

s.t

.Node 1 Flows

Node 2 Flows

Node 3 Flows

Node 4 Flows

Node 5 Flows

Node 6 Flows

Node 7 Flows

For all x_ij = 0, 1.

(b)

Find the shortest route from node 1 to node 7 in the network shown. (Enter your answers as a comma-separated list.)

path = 1, _____________ , 7