$($e$)$ Formulate a single linear programming model that simultaneously considers the shipping of $360$ million barrels of crude oil per year from the oil fields to the refineries $($including the new one in St$.$ Louis$)$ and the shipping of the final product from the refineries to the distribution centers. Use the objective of minimizing the grand total of all these shipping costs. Since the refineries collectively have a capacity of processing $390$ million barrels of crude oil per year, the decisions on the amount of crude oil each refinery will receive and process $($up to its capacity$)$ also is to be based on this same objective. Solve the model and compare the resulting total of all the shipping costs with the corresponding total calculated in parts $($b$)$ and $($d $)$ and from Table $7.$