Solve the linear programming problem by the method of corners.

Question

Solve the linear programming problem by the method of corners.

Maximize P = x + 2y
subject to x + y ≤ 4
               2x + y ≤ 5
               x ≥ 0, y ≥ 0

 

Maximum is p= ?? at (x,y)=?? 

Answer 1

Graph each inequality on the same grid. 2 of the lines are the 2 axes.  vertical axis (y>= 0) and Horizontal axis (x >= 0) so it is like telling you that you are looking on the 1st quadrant, all number positive.

Graph 2x + y <= 5,  so y <= -2x + 5

 

x + y <= 4 : so y<= -x + 4

 

Shade in the quadrilateral on the graph (possibly use a graphing calculator for the lines. You really do not need to shade in the quadrilateral but it looks nice. Anyway find the coordinates of the 4 corners and then plug them into the P= x + 2y equation and see which pair of numbers gives the maximum result.

 

(4,0) .... 4 + 2(0) =  4

(0, 0).... 0 + 0 = 0

(1,3).... 1 + 2(3) = 7

(2.5, 0).... 2.5 + 2(0)= 2.5

 

So the Max is 7  so the answer is (1,3)