2) Panini-ville is expecting the opening of a Delicious Sandwich restaurant in i

Question

2) Panini-ville is expecting the opening of a Delicious Sandwich restaurant in its town in 3 weeks. The mayor of Panini-ville wishes to avoid mass chaos in the streets. Therefore, the mayor has decided to restrict the flow of traffic through the town. Some streets will be blocked to one-way, while others will be open in both lanes. Numbers are given in the chart below representing thousands of cars that can travel each road each hours:

From

To

Flow Capacity

Reverse Flow Capacity

1

2

3

-

1

4

3

-

1

3

6

-

2

4

2

2

2

5

4

4

3

6

2

-

3

4

3

3

4

5

2

2

4

6

3

-

5

6

6

-

(a) How many vehicles can travel over each road before maximum flow is obtained? What is the maximal flow? Assume that the flow goes from 1 to 6, where 6 is the location of the new restaurant.

(b) Suppose that you (in place of the mayor) can open another road. This road has a flow of 4 thousand cars per hour, and cannot start or end at 6. Assuming this ONE road, where would you place the road in order to increase overall flow the most? Explain briefly.

2) Panini-ville is expecting the opening of a Delicious Sandwich restaurant in its town in 3 weeks. The mayor of Panini-ville wishes to avoid mass chaos in the streets. Therefore, the mayor has decided to restrict the flow of traffic through the town. Some streets will be blocked to one-way, while others will be open in both lanes. Numbers are given in the chart below representing thousands of cars that can travel each road each hours:

From

To

Flow Capacity

Reverse Flow Capacity

1

2

3

-

1

4

3

-

1

3

6

-

2

4

2

2

2

5

4

4

3

6

2

-

3

4

3

3

4

5

2

2

4

6

3

-

5

6

6

-

(a) How many vehicles can travel over each road before maximum flow is obtained? What is the maximal flow? Assume that the flow goes from 1 to 6, where 6 is the location of the new restaurant.

(b) Suppose that you (in place of the mayor) can open another road. This road has a flow of 4 thousand cars per hour, and cannot start or end at 6. Assuming this ONE road, where would you place the road in order to increase overall flow the most? Explain briefly.

Explanation / Answer

The question is about maximal flow from 1 to 6. Solution using excel solver is as follows:

I am unable to paste, The solution shows maximal flow of 11

1 to 2 flow 3, 1 to 4 flow 3, 1 to 3 flow 5 and final 3 to 6 flow 2, from 4 to 6 flow 3 and from 5 to 6 flow 6. So maximum 11 from 1 to 6.

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