Oilco produces two products: regular and premium gasoline. Each product contains 15 gram of lead per liter. The two products arc produced from six inputs: reformate, fluid catalytic cracker gasoline (FCG), isomerate (ISO), polymer (POL), MTBE (MTB), and butane (BUT). Each input has four attributes:
Attribute 1 | Research octane number (RON) |
Attribute 2 | RVP |
Attribute 3 | ASTM volatility at 70°C |
Attribute 4 | ASTM volatility at 130°C |
The attributes and daily availability (in liters) of each input arc given in Table 21.
The requirements for each output are given in Table 22.
The daily demand (in thousands of liters) for each product must be met, but more can be produced if desired. The RON and ASTM requirements arc minimums. Regular gasoline sells for 29.49¢/liter, premium gasoline for 3l.43¢. Before being ready for sale, .15 gram/liter of lead must be removed from each product. The cost of removing .1 gram/liter is 8.5¢. At most 38% of each type of gasoline can consist of FCG. Formulate and solve an LP whose solution will tell Oilco how to maximize their daily profit.‡
table 21
| Availability | RON | RVP | ASTM(70) | ASTM(130) |
Reformate | 15,572 | 98.9 | 7.66 | −5 | 46 |
FCG | 15,434 | 93.2 | 9.78 | 57 | 103 |
ISO | 6,709 | 86.1 | 29.52 | 107 | 100 |
POL | 1,190 | 97 | 14.51 | 7 | 73 |
MTB | 748 | 117 | 13.45 | 98 | 100 |
BUT | Unlimited | 98 | 166.99 | 130 | 100 |
table 22
| Demand | RON | RVP | ASTM(70) | ASTM(130) |
Regular | 9.8 | 90 | 21.18 | 10 | 50 |
Premium | 30 | 96 | 21.18 | 10 | 50 |
‡Based on Magoulas and Marinos-Kouris (1988).
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