Question

Standard Oil Company manufactures gasoline and jet fuel by using crude oil that costs $70 per barrel. Processing 1 barrel of crude oil requires 2 hours and yields 0.3 barrels of gasoline and 0.4 barrels of jet fuel. These products can be sold directly or can be purified to make higher quality products that sell for higher prices. One barrel of normal gasoline sells for $100 while further processing it for 3 hours and an additional cost of $30 will turn it into high quality gasoline that sells for $160. One barrel of normal jet fuel sells fon $110 while further processing it for 5 hours and an additional cost of $20 will turn it into high quality jet fuel which sells for $190. Assume he company has 5000 barrels of crude oil and 3000 hours of processing time available and is able to sell everything it produces.

Provide the optimization model that would maximize Standard Oil's profit

Answer 1

To maximize Standard Oil's profit, an optimization model includes decision variables for the quantities of gasoline and jet fuel, an objective function to maximize profit, and constraints on crude oil supply and processing time.

Step-by-step explanation:

The optimization model to maximize Standard Oil's profit from the production and sale of gasoline and jet fuel involves decision variables for the quantities of normal and high quality products, constraints on crude oil supply and processing time, and an objective function to maximize profit.

Let:

• x1 be the number of barrels of normal gasoline produced
• x2 be the number of barrels of high quality gasoline produced
• x3 be the number of barrels of normal jet fuel produced
• x4 be the number of barrels of high quality jet fuel produced

Objective Function:

Maximize Profit = ($100 * x1) + ($160 * x2) + ($110 * x3) + ($190 * x4) - ($70 * (x1 + x2 + x3 + x4) / 0.7) - ($30 * x2) - ($20 * x4)

Subject to constraints:

• Crude Oil supply: (x1 + x2 + x3 + x4) ≤ 5000 barrels
• Processing Time: (2 * (x1 + x2 + x3 + x4)) + (3 * x2) + (5 * x4) ≤ 3000 hours
• Product Ratios: x1 / 0.3 = x3 / 0.4
• Non-negativity: x1, x2, x3, x4 ≥ 0