The nodes represent important intersections in the network, the arrows represent one-way roads. The numbers indicate the capacity of each road in vehicles per second. The concession has been granted for 20 years, and the company has calculated that the total profit they obtain during the 20 years depends on the maximum flow that can circulate from node A to node E. The estimates made establish a profit of $ 500,000 USD for each vehicle per second that can circulate from A to E. The company is considering that with certain investments it would be possible to increase the capacity of the following routes:

Via	actual capacity	Posible increment	inversion required (USD)
B-C	5	3	$300,000
C-D	7	4	$400,000
C-E	3	3	$300,000
F-E	2	4	$400,000

If the extensions are carried out, the total investment of each one must be made, that is, if the BC highway is expanded, for example, the capacity would go from 5 to 8 cars per second, and the investment of $ 300,000 is subtracted from the profits, there is no partial extensions.

The capacity of the expanded roads will be equal to the current capacity plus the extension, if it is carried out. Solve the problem using Excel Solver or LINGO and answer the following questions:

a) The maximum profit that investors can achieve is: USD.

b) To achieve this maximum profit, the number of routes that would have to be expanded is: .

c) The maximum flow that can be transferred from A to E is: cars per second.

d) The flow that circulates through node C would be: cars per second.

8 3 9 4 5 E 8 3 9 3 8 8 3 9 4 5 E 8 3 9 3 8