I need help trying to set up a LP.
An oil refinery produces four types of raw gasoline: alkylate, catalytic cracked, straight-run, and isopentane. Two important characteristics of each gasoline are its performance number PN (also known as octane) and its vapor pressure RVP. The properties for each are alkylate has a PN of 107, RVP of 5, and can use 3814 Barrels/day. catalytic has a PN of 93, RVP of 8, and can use 2666 Barrels/day. straight-run has a PN of 87, RVP of 4 and can use 4016. Isopentane has a PN of 108, RVP of 21, and can use 1300. The four types of raw gasoline can be blended in Aviation Gas A, Aviation Gas B, or sold raw. When two kinds of gas are blended the PN and RVP of the blended gas is simply the weighted sum of the PN and RVP of the constituents. For example, if 1/3 barrel of Alkylate is mixed with 2/3 barrel of Catalytic-cracked gas, the resulting blend has PN=97.7 and RVP=7. Each of the four types of gas can be sold in raw form for \$4.83 per barrel. Aviation Gas A sells for \$6.45 per barrel. However, Aviation Gas A must have PN of at least 100 and RVP of at most 7. Aviation Gas B sells for \$5.91 per barrel but must have PN of at least 91 and RVP of at most 7. Formulate an LP that can be used to maximize the profit of the refinery.