Minimise: 3x + 2y Subject to: 2x+y<4 x>3 y>5 x,y>0 (a) Draw the feasible area. Ib) Does this linear programme have a solution? Explain your answer.

Question

Minimise: 3x + 2y

Subject to: 2x+y<4 x>3 y>5 x,y>0

 

(a) Draw the feasible area.

b) Does this linear programme have a solution? Explain your answer.

Answer 1

a) 2x + y < 4 can be rearranged to y < -2x +4. If you draw this line, it cuts the y-axis at +4, and the x-axis at +2. You can only have the area on the left of that line. Since x and y > 0, it is a triangle with the x and y axes as the other two sides.

 

x>3 means the area to the right of a vertical line at x = 3;

y>5 means the area above a horizontal line at y = 5

 

b) If you draw all that, you'll see that there is no area where all of those conditions are satisfied. So there is no solution.