Ten grades of crude are available in the quantities shown in the table ranging from $10,00030,000$ barrels per day each, with an aggregate availability of $200,000$ barrels per day. Refineries X$,$ Y$,$ and Z have incremental operations with stated requirements totaling $180,000$ barrels per day. Of the available crude, $20,000$ barrels per day is not used. One of the refineries can operate at two incremental operations, XI and X$2,$ which represent different efficiency levels. The net profit or loss for each crude in each refinery operationis given in the table in cents per barrel. It is assumed that the crude evaluations reflect the resulting product distribution from these incremental operations. $($In practice, however, if further debits are encountered in the solution because of lack of product quality or for transportation of surplus products, suitable corrections can be made in the crude evaluations and the problem reworked until a realistic solution is obtained.$)$ Maximize the profit per day by allocating the ten crudes among the three refineries with X being able to operate at two levels, so specify X$,$ and X$,$ as well as Y and Z$.$ Solve using MATLAB.