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 (indicating antiknock properties) and its vapor pressure RVP (indicating volatility). These two characteristics, together with the production levels in barrels per day, are as follows:

These gasolines can either be sold raw at $4.83 per barrel, or blended into aviation gasolines (Avgas A and/or Avgas B). Quality standards impose certain requirements on the aviation gasolines; these requirements, together with the selling prices are as follows:

85 barrels of isopentane are sold raw at S4.83 per barrel. Find the break-even selling prices for raw alkylate, catalytic, and straight-run. Next, assume there is a demand for Avgas C with PN at least 80 and RVP at most 7. Find the break-even selling price of this gasoline.

PN RVP Barrels produced 107 S 93 8 Alkylate Calalytic-cracked Straight-run Isopentane 3,814 2,666 7.016 1.300 87 + 108 21 PN RVP Price per barrel Avgas A Avgas B at least 100 at least 91 at most 7 at most 7 S6.45 $5.01 Variable names raw avgas A avgas B alkylate a r a A a B catalytic cur C_A CB straight sur SA SB isopentane ir iA i B production constraints: a_r + a A+ a B = 3814 Cr + CA + CB 2666 Sr + SA + SB ir + i A + i B 4016 = 1300 PN quality constraints: 107 a_A + 93 C_A + 87 S_A + 108 i_A ? 100 (a_A + C_A + s_A + i_A) 107 a B + 93 C B + 87 S B + 108 i B? 91 (a_B + C B + S_B + i_B) RVP quality constraints: 5 a A + 8 C_A + 4 S_A + 21 i_AS 7 (aA + C_A + S_A + i_A) 5 a_B + 8 C_B + 4 S_B + 21 i_B S 7 (a_B + C_B + S_B + i B) nonnegativity constraints: all variables 20. objective function = profit = 4.83 (a_r + cur + sur + i_r) + 6.45 (a_A + C_A + S_A + i_A) + 5.91 (a_B + C_B + S_B + i_B) PN RVP Barrels produced 107 S 93 8 Alkylate Calalytic-cracked Straight-run Isopentane 3,814 2,666 7.016 1.300 87 + 108 21 PN RVP Price per barrel Avgas A Avgas B at least 100 at least 91 at most 7 at most 7 S6.45 $5.01 Variable names raw avgas A avgas B alkylate a r a A a B catalytic cur C_A CB straight sur SA SB isopentane ir iA i B production constraints: a_r + a A+ a B = 3814 Cr + CA + CB 2666 Sr + SA + SB ir + i A + i B 4016 = 1300 PN quality constraints: 107 a_A + 93 C_A + 87 S_A + 108 i_A ? 100 (a_A + C_A + s_A + i_A) 107 a B + 93 C B + 87 S B + 108 i B? 91 (a_B + C B + S_B + i_B) RVP quality constraints: 5 a A + 8 C_A + 4 S_A + 21 i_AS 7 (aA + C_A + S_A + i_A) 5 a_B + 8 C_B + 4 S_B + 21 i_B S 7 (a_B + C_B + S_B + i B) nonnegativity constraints: all variables 20. objective function = profit = 4.83 (a_r + cur + sur + i_r) + 6.45 (a_A + C_A + S_A + i_A) + 5.91 (a_B + C_B + S_B + i_B)