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Linear Programming Problems

What is graph...

Question

What is a graphical method in linear programming?

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Solution

Graphical method in linear programming
Linear programming is a method of optimization of a linear function to find a solution for linear problems.
In linear programming, we use the graphical method to plot the points in the graph that satisfied the linear equations on the coordinate plane.

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Q. By graphical method, the solution of linear programming problem

Maximize Z = 3 x_{1} + 5 x_{2} Subject to 3 x_{1} + 2 x_{2} \leq 18 x_{1} \leq 4 x_{2} \leq 6 x_{1} \geq 0, x_{2} \geq 0, is

(a) x₁ = 2, x₂ = 0, Z = 6
(b) x₁ = 2, x₂ = 6, Z = 36
(c) x₁ = 4, x₂ = 3, Z = 27
(d) x₁ = 4, x₂ = 6, Z = 42

Q. Show the solution of the problem of linear programming under the following restrictions by graphical method:

x + y \leq 4, x \geq 0, y \geq 0

Q. Solve the linear programming problem by graphical method with the following restrictions.

3 x + 5 y \leq 5; 5 x + 2 y \leq 10; x \geq 0, y \geq 0

Z = 5 x + 3 y

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Q. By graphical method solve the following linear programming problem for minimization:
Objective function constraints

Z = 5 x + y

3 x + 5 y \geq 5

5 x + 2 y \leq 10

x \geq 0, y \geq 0

Q. By graphical method solve the following linear programming problem for maximization.
Objective function Z = 1000 x + 600 y
Constraints

x + y \leq 200

4 x - y \leq 0

x \geq 20, x \geq 0, y \geq 0

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Linear Programming Problems

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