Final answer:
The maximum value of the function F=5x+2y under the given constraints is found by graphing the inequalities to define the feasible region, identifying the corner points, evaluating F at each, and determining the coordinates (x, y) where the maximum occurs.
Step-by-step explanation:
To find the maximum value of the objective function F = 5x + 2y, given the constraints:
- x + 2y < 6
- x ≥ 0
- y ≥ 0
- 2x + y ≤ 6
We will use the method of linear programming. This involves plotting the feasible region defined by the constraints on a graph, and then finding the corner points of this region. The maximum value of the objective function will occur at one of these corner points.
Step 1: Graph the inequalities to define the feasible region.
Step 2: Identify the corner points of the feasible region by finding the intersection of the lines.
Step 3: Evaluate the objective function F at each corner point to find the maximum value.
Step 4: Identify the values of x and y where this maximum occurs.