Optimization in Resource Allocation?

📌 CONCEPT: Optimization in Resource Allocation is the process of determining the best way to allocate limited resources to maximize the overall benefit or utility.

📐 RULE / FORMULA: The optimal allocation of funds between two projects can be determined by maximizing the total utility function, subject to the constraint that the total cost of both projects does not exceed the available funds. In mathematical terms, let x be the amount allocated to the first project and y be the amount allocated to the second project, then we want to maximize the utility function U(x, y) subject to the constraint 2x + y ≤ 5.

💡 WORKED EXAMPLE: Consider the town council's allocation problem. Let x be the amount allocated to the new hospital wing and y be the amount allocated to the new healthcare center. We want to maximize the total utility function U(x, y) = (2x + 0.8y) + (y + 0.5y), subject to the constraint 2x + y ≤ 5. To solve this problem, we can use the graphical method or the simplex method to find the optimal values of x and y.

⚠️ COMMON MISTAKE: Students often confuse the utility function with the cost function, or forget to consider the constraint when maximizing the utility function.