Скачать или смотреть Solve Linear Programming with Graphical & GAMS Methods Empty, Point & 2D Feasible Regions

Welcome to this step‑by‑step Linear Programming (LP) tutorial, where we solve a unique optimization problem using two powerful approaches: the Graphical Method and GAMS (General Algebraic Modeling System).

📌 The Problem
We aim to minimize the following objective function:

Max Z=5x1+3x2
s.t.
x1+x2=l=6
x1=g=3
x2=g=3
2x1+3x2=g=3
x1,x2=g=0

This is a simple LP model with two decision variables and one main constraint (plus non‑negativity conditions). However, what makes this example special is that, by changing the right‑hand side of the first constraint, we explore three distinct feasibility scenarios.

📊 Three Feasibility Cases
Empty Feasible Region – No solution satisfies all constraints.
Point Feasible Region – Only a single point satisfies all constraints.
Two‑Dimensional Feasible Region (Feasible Line Case) – The feasible region lies along a line, not a typical polygonal area.
Understanding these cases deepens your insight into geometric interpretations of LP problems and how constraint changes can completely alter the solution space.

💡 What You Will Learn
Graphical Method:
Plotting constraints in 2D space.
Identifying feasibility cases visually.
Locating the optimal solution graphically.
GAMS Method:
Writing the LP model in GAMS syntax.
Running the solver and interpreting results.
Comparing results with the graphical method.

🎯 Why This Video Is Worth Watching
Covers two complementary solution methods in one lesson.
Explains rare cases like feasible line and point feasibility.
Perfect for students, researchers, and professionals in optimization, operations research, and applied mathematics.
Combines visual learning with professional solver application.

🧠 Who Should Watch
Engineering, economics, and mathematics students.
Operations research practitioners.
Anyone learning optimization and LP modeling.

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