If $4V6$ then formulate the following 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:

$\backslash$table$[[\backslash$table$[[$Process$],[$plant$]],\backslash$table$[[$Capacity of the plant$],[$ day$)]],\backslash$table$[[$Production cost $(\frac{\text{\$}}{?}$ day$)$ to$],[$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$),50,150,100,75],[$Penalty $($per each kilogallon shortage$),$$$10,$$$12,$$$16,$$$20$