The vertices of the closed convex polygon determined by the...

The vertices of the closed convex polygon determined by the inequations $3 \mathrm{x}+2 \mathrm{y} \geq 6,4 \mathrm{x}+3 \mathrm{y} \leq 12$ $\mathrm{x} \geq 0$ and $\mathrm{y} \geq 0$ are (1) $(1,0),(2,0),(0,2),(0,1)$ (2) $(2,0),(3,0),(0,4)$ and $(0,3)$. (3) $(1,0),(2,0),(0,2)$ and $(2,2)$. (4) $(1,0),(0,2),(2,2)$ and $(1,1)$.

The vertices of the closed convex polygon determined by the inequations $3 \mathrm{x}+2 \mathrm{y} \geq 6,4 \mathrm{x}+3 \mathrm{y} \leq 12$ $\mathrm{x} \geq 0$ and $\mathrm{y} \geq 0$ are
(1) $(1,0),(2,0),(0,2),(0,1)$
(2) $(2,0),(3,0),(0,4)$ and $(0,3)$.
(3) $(1,0),(2,0),(0,2)$ and $(2,2)$.
(4) $(1,0),(0,2),(2,2)$ and $(1,1)$.

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Key Concepts

Convex Polygon

A convex polygon is a closed, convex shape where every line segment joining any two points in the polygon lies completely within the polygon. The feasible region in linear programming often forms a convex polygon, which is important for ensuring the uniqueness and efficiency of optimization solutions.

Intersection of Lines

Finding the intersection points of the boundary lines of the linear inequalities is crucial, as these intersections are the vertices of the feasible region. They are determined by solving pairs of linear equations.

Feasible Region

The feasible region is the common area where all the half-planes defined by a system of linear inequalities overlap. It represents all the possible solutions that satisfy the entire set of constraints.

Linear Inequalities

Linear inequalities are expressions involving two variables with inequality symbols. They represent half-planes on the coordinate plane, and together they define constraints that all solutions must satisfy.

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