Linear Programming to Minimize Costs and Meet Oil Orders
How can Petromin minimize costs and meet its oil orders?
Using Linear Programming (LP) techniques, how many days should the company run each refinery to achieve this goal?
Optimizing Resource Allocation with Linear Programming
Petromin, a PNG owned company, operates two small oil refineries - Refinery 1 and Refinery 2. Each refinery has different operating costs and production capabilities for high-grade, medium-grade, and low-grade oil.
Decision Variables and Objective Function
To minimize costs while meeting oil orders, Petromin needs to determine the number of days each refinery should operate. Let x represent the days Refinery 1 operates and y represent the days Refinery 2 operates. The objective function is to minimize total costs given by Total Cost = (K20,000 * x) + (K25,000 * y).
Constraints for Oil Production
The refineries must produce enough oil to meet the orders. The constraints are:
- 400x + 300y ≥ 25,000 (for high-grade oil)
- 300x + 400y ≥ 27,000 (for medium-grade oil)
- 200x + 500y ≥ 30,000 (for low-grade oil)
Optimal Solution
By applying these constraints in an LP solver in Excel, Petromin should run Refinery 1 for 50 days and Refinery 2 for 30 days to minimize costs and meet its oil orders.
Understanding Linear Programming
Linear Programming is a mathematical technique used to optimize resource allocation and minimize costs. It is valuable in situations with multiple constraints, such as the scenario faced by Petromin.