General Gurobi model code for MCNF $1.$ An oil company has oil fields in San Diego and Los Angeles. The San Diego field can produce up to $500,000$ barrels per day, and the Los Angeles field can produce up to $400,000$ barrels per day. Oil is sent from the fields to a refinery, either in Dallas or in Houston $($assume each refinery has unlimited capacity$).$ To refine $1,000$ barrels costs $\backslash (\backslash$$ $700\backslash )$ at Dallas and $\backslash (\backslash$$ $900\backslash )$ at Houston. Refined oil is shipped to customers in Chicago and New York. Chicago customers require $400,000$ barrels per day and New York customers require $300,000$ barrels per day. The costs of shipping $1,000$ barrels of oil $($refined or unrefined$)$ is given in the table below. The goal is to minimize the total cost of meeting all demands.

$($a$)$ Draw the graph of a balanced minimum cost network flow $($MCNF$)$ problem that represents this problem. Write down the corresponding numbers next to the nodes and arcs, and briefly explain what they mean.

$($b$)$ Write down the generic data$-$independent linear programming formulation of an MCNF problem $($with capacity constraints$)$ and write down the data for this particular problem separately.

$($c$)$ Write a data$-$independent Gurobi model for MCNF in general. Look at the lecture notes and code to learn about the Gurobi syntax.

$($d$)$ Solve the problem with Gurobi. Report the optimal solution in your written assignment, by drawing a graph corresponding to the optimal solution. Submit your Gurobi files as usual.