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Linear Programming Example 1

Linear Programming Example 1
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2020-01-20 01:02
Coordinate GeometryOptimizationGeometric Construction
In collections Discrete: Linear Programming
This example demonstrates the geometric solution method for linear programming problems, visually showing the process of finding the optimal solution. Core math concepts include linear inequalities, feasible regions, optimal solutions, and convex polygons. It uses GeoGebra objects a, b, c, d, e, text1, likely involving line drawing, region highlighting, and labeling. Suitable for high school and above students to understand the application of linear programming in real-world problems.

GeoGebra Commands & Parameters

  1. a(x, y) = (2 * x) + y ≥ 20
  2. b(x, y) = x + (2 * y) ≥ 12
  3. c(x, y) = x + (3 * y) ≥ 15
  4. d(x) = x ≤ 0
  5. e(y) = y ≤ 0

AI Drawing Prompt Reference

Draw a coordinate system and plot three lines corresponding to the equations 2x+y=20, x+2y=12, and x+3y=15, shade the feasible region formed by the intersection of these lines, which is on the left side of the x-axis and below the y-axis, and label the optimal solution point within the shaded area.
The prompt above was compiled from the original drawing commands and is for reference only.