$2\mathrm{.}5$ Oil Blending: An oil company produces three brands of oil: regular, multigrade, and supreme. Each brand of oil is composed of one or more of four crude stocks, each having a different lubrication index. The relevant data concerning the crude stocks are as follows.

Crude Stock Lubrication Index Cost $($$$/$Barrel$)$

$1207\mathrm{.}12408\mathrm{.}53307\mathrm{.}74559$

Daily Supply $($Barrels$)$

$1000110012001100$

Each brand of oil must meet a minimum standard for a lubrication index, and each brand thus sells at a different price. The relevant data concerning the three brands of oil are as follows.

Brand

Regular Multigrade Supreme

Minimum Lubrication Index

$253550$

Selling Price $($$$/$Barrel$)$

$8\mathrm{.}5910$

Daily Demand $($Barrels$)$

$20001500750$