$\backslash$table$[[$Vegetable oils,VEG $1],[,$VEG $2],[$Non$-$vegetable oils,OIL $1],[,$OIL $2],[,$OIL $3]]$

Each oil may be purchased for immediate delivery $($January$)$ or bought on the futures market for delivery in a subsequent month. Prices at present and in the futures market are given below in $(\frac{}{?}$ ton$)$:

$\backslash$table$[[,$VEG $1,$VEG $2,$OIL $1,$OIL $2,$OIL $3],[$January$,110,120,130,110,115],[$February$,130,130,110,90,115],[$March$,110,140,130,100,95],[$April$,120,110,120,120,125],[$May$,100,120,150,110,105],[$June$,90,100,140,80,135]]$

The final product sells at $150$ per ton.

Vegetable oils and non$-$vegetable oils require different production lines for refining. In any month, it is not possible to refine more than $200$ tons of vegetable oils and more than $250$ tons of non$-$vegetable oils. There is no loss of weight in the refining process, and the cost of refining may be ignored.

It is possible to store up to $1000$ tons of each raw oil for use later. The cost of storage for vegetable and non$-$vegetable oil is $5$ per ton per month. The final product cannot be stored, nor can refined oils be stored.

There is a technological restriction of hardness on the final product. In the units in which hardness is measured, this must lie between $3$ and $6.$ It is assumed that hardness blends linearly and that the hardnesses of the raw oils are

$\backslash$table$[[$VEG $1,8\mathrm{.}8],[$VEG $2,6\mathrm{.}1],[,],[$OIL $1,2\mathrm{.}0],[$OIL $2,4\mathrm{.}2],[$OIL $3,5\mathrm{.}0]]$