Solve the linear programming problem by the method of corner

Solve the linear programming problem by the method of corners. Maximize P = 3x + 7y subject to 2x + y lessthan equal 16 2x + 3y lessthan equal 24 y lessthan equal 5 x greaterthan equal 0, y greaterthan equal 0 (x, y) = ( The maximum is P = at ).

Solution

Feasible region:

Corner points are:

(0, 0) (0, 5) (8, 0) (4.5, 5) (6, 4)

Plug each corner point into profit function:

Corner point   (x, y)

Therefore, profit is maximum at a corner point (4.5, 5)

Thus, (x, y) = (4.5, 5)

P = $48.5

Corner point   (x, y)	P = 3x + 7y	Profit (P)
(0, 0)	P = 3*0 + 7*0	P = 0
(0, 5)	P = 3*0 + 7*5	P = 35
(8, 0)	P = 3*8 + 7*0	P = 24
(4.5, 5)	P = 3*4.5 + 7*5	P = 48.5
(6, 4)	P = 3*6 + 7*4	P = 46