Linear Programming to Maximize Profit for Sunco Oil

How can Sunco Oil maximize its profit by using linear programming?

To maximize Sunco's profit, what factors need to be considered when determining the optimal mix of processes?

Solution:

To maximize profit, Sunco Oil must calculate the profit per hour for each of its three processes, operating within the constraints of available crude oils, operational hours, and then determine the optimal mix of processes using methods like linear programming.

To maximize Sunco Oil's profit, we need to consider the costs of running each process, the input of crude oils required, the output of gasoline produced, and the selling price of each type of gasoline. We also have to take into account the monthly limitations: 4000 barrels of crude 1 at $45 per barrel, 7000 barrels of crude 2 at $55 per barrel, and 2500 hours of operation on the catalytic cracker.

Processes:

Process 1: Costs $20/hour, uses 2 barrels of crude 1 and 3 barrels of crude 2, produces 2 barrels of gas 1 (sold at $85/barrel) and 1 barrel of gas 2 (sold at $90/barrel).

Process 2: Costs $30/hour, uses 1 barrel of crude 1 and 3 barrels of crude 2, produces 3 barrels of gas 2.

Process 3: Costs $14/hour, uses no crude oil but 3 barrels of gas 2, produces 2 barrels of gas 3 (sold at $95/barrel).

To maximize profit, Sunco should first calculate the profit per hour for each process considering the cost of the crude oils, operation costs, and the revenue from sold gasoline. Then, they need to work within the constraints of available crude oils and operational hours. The company might use linear programming or simplex algorithm to find the optimal mix of processes that yields the highest profit.