Consider a computer network consisting of six computers, A through $F.$ The computers are

connected according to the following links, with maximum data rates $($in Mbps$)$ shown: AC

$(10),$ BC $(7),$ BF $(3),$ CD $(8),$ DE $(12),$ DF $(4).$ For example, AC $(10)$ means that computers

A and $C$ are connected with a link that supports data rates up to $10Mbps.$

Suppose that A and B need to send data to E and F$,$ respectively $($no other communication

is taking place in the network$).$ Any path through the given links above may be used as long

as the path has no loop. Also, multiple paths $($say from A to E$)$ can be used simultaneously.

Link bandwidth can be shared as long as the total data rate through the link does not exceed

its maximum $($the total data rate through a link is the sum of the data rates of communication

in both directions$).$

For every Mbps of data rate the network can support for transmission from A to E$,$ we receive $2$

dollars. For every Mbps of data rate the network can support for transmission from B to F$,$ we

receive $3$ dollars. Formulate a linear programming problem to represent the goal of maximizing

the total revenue. Then, convert this problem into standard form.