Answer :
The valid objective function is (3)f(x, y) = 25x + 20y.
To determine which of the presented options is a valid objective function, we need to understand what an objective function is. An objective function is typically used in optimization problems and is a function of the variables in the problem that needs to be optimized (maximized or minimized).
- 5x + 3y ≤ 150: This is an inequality constraint, not an objective function.
- x - y = 10: This is an equality constraint, not an objective function.
- f(x, y) = 25x + 20y: This is a correct example of an objective function as it represents a model to be maximized or minimized.
- x ≥ 25: This is an inequality constraint, not an objective function.
Therefore, the correct answer is f(x, y) = 25x + 20y. Objective functions play a crucial role in mathematical optimization problems, often subject to various constraints.
