Question

answer both parts for the question on excel with formulas and solver function. show all steps with screen shots of excel please and thank you!

I. The North-South highway system passing through Albany can accommodate the capacities as shown below (numbers are in '000s vehicles per hour). What is the maximum flow that can be handled between a) points 1 and 6 b) points and 5 For both the above cases, what would be required to increase the capacity by 1000 vehicles per hour?

Answer 1

1. Let Xij denote the number of vehicles from node i to node j.

Therefore the objective function:

• Max z= X61

The conservation of flow constraint for the six nodes:

Node 1: X12 + X13 + X14 – X61 = 0

Node 2: X24 + X25 -X12 – X42 = 0

Node 3: X34 + X36 -X13 – X43 = 0

Node 4: X42 + X43 + X45 + X46 -X14 – X24 – X34 – X54 = 0

Node 5: X54 + X56 -X25 – X45 = 0

Node 6: X61 – X36 - X46 – X56 = 0

• Note: +ve Flow out –ve Flow in

Additional constraint needed to enforce the capacities on the arcs. These simple upper-bound constraints are given.

• X12 ≤ 2
• X13≤ 4
• X14≤ 3
• X24≤ 1
• X25≤ 3
• X34≤ 2
• X36≤ 2
• X42≤ 1
• X43≤ 2
• X45≤ 2
• X46≤ 3
• X56≤ 4

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