Please use LINGO to answer the question and provide the code! Please only post after you ran it on LINGO to make sure it was correct!! Consider using this to help: @for$($note$($j$)$: @sum$($edge$($i$,$j$)$: inflow$($i$,$j$))=$@sum$($edge$($j$,$k$)$: outflow$($j$,$k$))$

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The High$-$Price Oil Company owns a pipeline network that is used to convey oil from its

source to several storage locations. A portion of the network is as follows:

Due to the varying pipe sizes, the flow capacities vary. By selectively opening and closing

sections of the pipeline network, the firm can supply any of the storage locations.

a$.$ If the firm wants to fully utilize the system capacity to supply location $7,$ how long will

it take to satisfy a location $7$ demand of $100,000$ gallons? What is the maximal flow for

this pipeline system?

b$.$ If a break occurs on line $2-3$ and that line is closed down, what is the maximal flow for

the system? How long will it take to transmit $100,000$ gallons to location $7?$