How to solve this Linear Programming problem graphically

In summary, the conversation is about solving an LP problem graphically by drawing lines for the equations, shading the excluded regions, and checking the corners to find the optimal solution. The question also mentions changing the objective function from minimization to maximization and how it affects the optimal solution.
  • #1
ashina14
34
0

Homework Statement



Solve the following LP problem GRAPHICALLY

Minimise -x1+x2
subject to constraints x1+x2 >=1,
x1+2x2<=8,
x1-x2<=5,
x1>=0, x2>=0.

a)by sketching the feasible set
b)finding optimal solutions of this LP problem. What is the optimal value of the objective function?
c) If the objective is changed to 'maximise -x1_x2' then how does the optimal solution change?



Homework Equations





The Attempt at a Solution



Do I just draw lines for all the equations, then choose 'corner points' and see if they satisfy each equation then shade the right area?
 
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  • #2
Draw lines, shade the excluded regions. The remaining area satisfies all inequalities, and you can check the corners.
 
  • #3
Thanks that's what I did!
 

Related to How to solve this Linear Programming problem graphically

1. What is Linear Programming?

Linear Programming is a mathematical method used to optimize a linear objective function, subject to a set of linear constraints. It is commonly used in business and economics to make the best use of limited resources.

2. How do I solve a Linear Programming problem graphically?

To solve a Linear Programming problem graphically, you will need to plot the constraints on a graph and then find the feasible region. Next, plot the objective function and find the point where it is maximized or minimized within the feasible region. This point is the optimal solution to the problem.

3. What is the difference between a feasible region and an optimal solution?

A feasible region is the area on the graph that satisfies all of the given constraints. An optimal solution is the point within the feasible region that maximizes or minimizes the objective function. In other words, it is the solution that provides the best possible outcome.

4. Can a Linear Programming problem have multiple optimal solutions?

Yes, a Linear Programming problem can have multiple optimal solutions. This typically occurs when the objective function is parallel to one of the constraints, resulting in multiple points where the function is maximized or minimized within the feasible region.

5. What are the limitations of solving a Linear Programming problem graphically?

Solving a Linear Programming problem graphically can become time-consuming and difficult when dealing with a large number of variables and constraints. Additionally, graphical solutions may not be as accurate as other methods, such as the simplex algorithm, and cannot be used for non-linear problems.

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