How to solve this Linear Programming problem graphically

[ashina14]

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?

 

[mfb]

Draw lines, shade the excluded regions. The remaining area satisfies all inequalities, and you can check the corners.

 

[ashina14]

Thanks that's what I did!