Maximizing Profit in Oil Refinery Production

What is the maximum total profit that can be realized daily?

The maximum production of an oil refinery is 1600 barrels per day, with production costs and profits for gasoline and heating oil given. What is the optimal strategy to maximize daily profit?

Final answer:

The refinery should prioritize producing the more profitable heating oil. Under the constraints of the daily budget and production capacity, the maximum daily profit is attained by producing 1600 barrels of heating oil, yielding a profit of $8000 per day.

The oil refinery's production capacity is limited to 1600 barrels per day, which can be divided between gasoline and heating oil. The production cost per barrel is $8 for gasoline and $9 for heating oil, with a daily budget of $9600. To maximize profit, we need to determine the optimal production mix that yields the highest total profit within these constraints.

We can create equations based on the production costs, production capacity, and profit margins of gasoline and heating oil. Let G be the number of barrels of gasoline and H be the number of barrels of heating oil. The cost constraint is 8G + 9H ≤ 9600, and the production capacity constraint is G + H ≤ 1600.

Maximizing the total daily profit (F), which is given by F = 4G + 5H, involves finding the combination of gasoline and heating oil production that maximizes this expression. Since heating oil has a higher profit margin, the refinery should prioritize producing more heating oil to maximize profit.

By solving the optimization problem, we find that producing 1600 barrels of heating oil results in the maximum daily profit of $8000. This approach ensures that the refinery operates efficiently and maximizes its profitability within the given constraints.