What point in the feasible region maximizes the objective function?Constraints: x≥0y≥0−x+3≥yy≤13x+1 Objective function: C = 5x – 4y explain in simple

Answer 1

The feasible region is the possible solutions to the system of inequalities. The given constraints are: x≥0, y≥0, −x+3≥y, y≤13x+1.

To find the point in the feasible region that maximizes the objective function, we need to evaluate the objective function at each corner point of the feasible region and see which one gives the highest value.

We'll start by graphing the constraints to determine the feasible region's shape and corner points.

First, let's draw the lines x=0 and y=0. These represent the x≥0 and y≥0 constraints, respectively. These lines divide the coordinate plane into four quadrants.

Next, let's draw the line −x+3=y. This represents the −x+3≥y constraint. This line has a slope of -1 and a y-intercept of 3. We can plot two points: (0, 3) and (3, 0), and then connect them with a line.

Finally, let's draw the line y=13x+1. This represents the y≤13x+1 constraint. This line has a slope of 13 and a y-intercept of 1. We can plot two points: (0, 1) and (1/13, 2), and then connect them with a line.

Now, we need to find the points where these lines intersect to identify the corner points of the feasible region. After examining the graph, we find the following corner points: (0, 3), (0, 1), (1/13, 2).

Now we evaluate the objective function, C=5x-4y, at each of these corner points.

For the point (0, 3): C = 5(0) - 4(3) = -12.
For the point (0, 1): C = 5(0) - 4(1) = -4.
For the point (1/13, 2): C = 5(1/13) - 4(2) ≈ -7.077.

From these values, we can see that the point (0, 3) gives the maximum value for the objective function. Therefore, the point (0, 3) in the feasible region maximizes the objective function.