What point in the feasible region maximizes the objective function.
Constraints:
x ≥ 0
y ≥ 0
-x + 3 ≥ y
y ≤ 1/3x +1
Objective function: c = 5x - 4y
To find the point in the feasible region that maximizes the objective function, we need to find the corner point where the objective function takes its maximum value.
First, let's graph the constraints to determine the feasible region.
The constraint "-x + 3 ≥ y" can be rewritten as "y ≤ -x + 3", which represents a line with a slope of -1 and a y-intercept of 3.
The constraint "y ≤ 1/3x +1" represents a line with a slope of 1/3 and a y-intercept of 1.
Since the constraints are inequalities, we need to shade the area below the lines to represent the feasible region.
[Graph of the feasible region]
To find the corner point that maximizes the objective function, we need to evaluate the objective function at the corner points of the feasible region.
The corner points of the feasible region are the intersections of the lines representing the constraints. From the graph, the corner points are (0, 1), (3, 0), and (1.5, 1.5).
Let's evaluate the objective function at these points:
1. (0, 1): c = 5(0) - 4(1) = -4
2. (3, 0): c = 5(3) - 4(0) = 15
3. (1.5, 1.5): c = 5(1.5) - 4(1.5) = 0
From the evaluations, we can see that the objective function takes its maximum value of 15 at the point (3, 0) in the feasible region.