Three refineries send a gasoline product to two distribution terminals through a pipeline network. Any demand that cannot be satisfied through the network is acquired from other sources. The pipeline network is served by three pumping stations, as shown in Figure $6\mathrm{.}41.$ The product flows in the network in the direction shown by the arrows. The capacity of each pipe segment $($shown directly on the arcs$)$ is in million bbl per day. Determine the following:

$($a$)$ The daily production at each refinery that matches the maximum capacity of the network.

$($b$)$ The daily demand at each terminal that matches the maximum capacity of the network.

$($c$)$ The daily capacity of each pump that matches the maximum capacity of the network.

$($d$)$ Model the problems as a linear program, then solve using Solver

FIGURE $6\mathrm{.}41$

Network for Problems $6-31$

and $6-32$