Problem

An oil refinery produces four grades of motor oil in three process plants. The refinery incurs a penalty for not meeting the demand of any particular grade of motor oil. The capacities of the plants, the production costs, the demands of the various grades of motor oil, and the penalties are given in the following table. The goal is to minimize the overall cost.

$\backslash$table$[[,,\backslash$table$[[$Production cost $($$$/$day$)$ to$],[$Process$],[$plant$]],\backslash$table$[[$Capacity of the plant$],[($kgal$/$day$)]],\backslash$table$[[$manufacture motor oil of grade:$]],1,2,3,4],[1,100,750,900,1000,1200,,,,,,,],[2,150,800,950,1100,1400,,,,,,,],[3,200,900,1000,1200,1600,,,,,,,],[,,,,,,,,,,,,],[$Demand $($kgal$/$day$),50,150,100,75,,,,,,,,],[$Peralty $($per each kilogallon shortage$),$$$10,$$$12,$$$16,$$$20,,,,,,,,]]$ki