Final answer:
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.