There are two sorts of petrol, regular and premium, obtained by blending the naphtha, reformed gasoline and cracked gasoline. The only stipulations concerning them are that regular must have an octane number of at least 84 and that premium must have an octane number of at least 94. It is assumed that octane numbers blend linearly by volume.
The stipulation concerning jet fuel is that its vapour pressure must not exceed 1 kilogram per square centimetre. The vapour pressures for light, heavy and cracked oils and residuum are 1.0, 0.6, 1.5 and 0.05 kilograms per square centimetre respectively. It may again be assumed that vapour pressures blend linearly by volume.
To produce fuel oil, light oil, cracked oil, heavy oil and residuum must be blended in the ratio 10:4:3:1.
There are availability and capacity limitations on the quantities and processes used:
The daily availability of crude 1 is 20,000 barrels.
The daily availability of crude 2 is 30,000 barrels.
At most 45,000 barrels of crude can be distilled per day.
At most 10,000 barrels of naphtha can be reformed per day.
At most 8000 barrels of oil can be cracked per day.
The daily production of lube oil must be between 500 and 1000 barrels.
Premium motor fuel production must be at least 40% of regular motor fuel production.
The profit contributions from the sale of the final products are (in pence per barrel)
|
Premium petrol |
700 |
|
Regular petrol |
600 |
|
Jet fuel |
400 |
|
Fuel oil |
350 |
|
Lube-oil |
150 |
How should the operations of the refinery be planned in order to maximize total profit?