Solve the linear programming problem by the method of corners.

Question

Solve the linear programming problem by the method of corners.

Maximize P = 2x + 4y

subject to 2x + y ≤ 16
              2x + 3y ≤ 24
               y ≤  7
              x ≥ 0, y ≥ 0

 

Maximum is P= ??? at (x, y)= ?? 

 

Answer 1

Graph the 5 lines on one grid. Find the Pentagon and the coordinates of the corner points. Take the corner points and plug into the P equation. See which answer is largest.

 

I graphed the lines and got the 5 corner points of the pentagon to be:

 

(0,0)..... 2 (0) + 4(0) = 0

(0, 7)..... 2 (0) + 4 (7) = 28

(1.5, 7) ... 2 (1.5) + 4 (7) = 31

(6,4).... 2 (6) + 4 (4) = 28

(8, 0).... 2(8) + 4(0)= 16

 

So the MAX is 31 and the ordered pair is (1.5, 7)