Corner Point Calculator

Point 1 (x1, y1): Point 2 (x2, y2):

To provide an example, let's consider a simple linear programming problem with two variables:

Maximize Z = 3x + 2y

Subject to the following constraints:

1. 2x + y ≤ 20
2. 4x - 5y ≥ -10
3. x, y ≥ 0

To find the corner points of the feasible region, we can set up and solve the system of linear inequalities. Here's how you might approach this:

1. Plot the constraints on a graph:
   • Draw the lines representing the inequalities and shade the feasible region.
2. Identify the corner points:
   • The corner points are the intersections of the lines that form the boundaries of the feasible region.
3. Solve for the coordinates of the corner points:
   • Solve the system of equations formed by the lines intersecting at each corner point.

Let's solve this example:

Constraint 1: 2x + y ≤ 20

The line is 2x + y = 20.

Constraint 2: 4x - 5y ≥ -10

The line is 4x - 5y = -10.

Plotting on a graph:

Feasible Region
      /\
     /  \
    /    \
   /      \
  /        \
 /__________\

Corner Points:

The intersections of the lines form the corner points of the feasible region.

Let's say there are three corner points: A, B, and C.

Solving for the coordinates:

Solve the system of equations for each corner point to find their coordinates.

For example, if A is the intersection of the lines 2x + y = 20 and 4x - 5y = -10, solve this system to find the values of x and y at point A.

Repeat this process for each corner point.

Keep in mind that this is a basic example, and in more complex problems, you might need to use linear programming software or tools to find corner points numerically.

Corner Point Calculator