Exercise 1.16 A manager of an oil refinery has 8 million barrels of crude oil A

Question

Exercise 1.16 A manager of an oil refinery has 8 million barrels of crude oil A and 5 million barrels of crude oil B allocated for production during the coming month. These resources can be used to make either gasoline, which sells for $38 per barrel, or home heating oil, which sells for $33 per barrel. There are three production processes with the following characteristics: Process 1 Process 2 Process 3 Input crude A Input crude B Output gasoline Output heating oil $40 $51 $11 Cost All quantities are in barrels. For example, with the first process, 3 barrels of crude A and 5 barrels of crude B are used to produce 4 barrels of gasoline and

Explanation / Answer

Solution:

We introduce variables x1, x2 and x3 for the three production processes.
Since the amount of crude A is limited by 8 million barrels, we get the constraint
   3x1 + x2 +5x3 8.
Similarly, we get the constraint
   5x1 + x2 +3x3 5
for crude B.
The net revenue (in millon $) is given as
   38 ·(4x1 + x2 +3x3)+33 ·(3x1 + x2 +4x3)51x1 11x2 40x3.
This can be simplified to
   200x1 +60x2 +204x3.

Thus the linear program is given as:
   max 200x1 +60x2 +204x3
   subject to 3x1 + x2 +5x3 8
   5x1 + x2 +3x3 5
   x1,x2,x3 0

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