Question

An Oil refinery has two sources of crude oil: A light crude oil that cost 35$/barrel and a heavy crude that costs $30/barrel. The refinery produces gasoline, heating oil, and jet fuel from crude in the amounts per barrel indicated in the following table

Gasoline Heating Oil Jet Fuel
light .3 .2 .3
heavy .3 .4 .2
The refinery has contracted to supply 900000 barrels of gasoline, 800000 barrels of heating oil, and 500000 barrels of jet fuel. The refinery wishes to find the amounts of light and heavy to purchase so as to able to meet its obligations at minimum costs. Formulate this problem as a linear programming problem.

Answer 1

The student's question about an oil refinery's production problem can be framed as a linear programming problem to minimize costs, with constraints based on the production capacity of gasoline, heating oil, and jet fuel from light and heavy crude oil.

Step-by-step explanation:

The student is dealing with a problem that requires the use of linear programming to minimize cost while fulfilling production requirements in an oil refinery. The question involves two raw materials (light and heavy crude oil) and three products (gasoline, heating oil, and jet fuel). Each type of crude oil produces a different amount of each product per barrel.

Objective Function: Minimize cost = 35x + 30y
Where x = barrels of light crude oil and y = barrels of heavy crude oil.

Constraints:
0.3x + 0.3y ≥ 900,000 (Gasoline)
0.2x + 0.4y ≥ 800,000 (Heating Oil)
0.3x + 0.2y ≥ 500,000 (Jet Fuel)
x, y ≥ 0 (Non-negativity)

This formulation assists the refinery in determining the optimal mix of light and heavy crude to meet product obligations at the lowest possible cost. It includes the calculation of the required quantities of crude oil to produce the desired amount of each fuel product while adhering to budget constraints.