Solve the linear programming problem by the method of corners. Maximize subject to
A) x = 1; y = 2; P = 9
B) x = 1; y = 3; P = 13
C) x = 0; y = 3; P = 12
D) x = 0; y = 4; P = 16

Question

Solve the linear programming problem by the method of corners. Maximize   subject to    
A) x = 1; y = 2; P = 9 
B) x = 1; y = 3; P = 13 
C) x = 0; y = 3; P = 12 
D) x = 0; y = 4; P = 16

Quizplus · Accepted Answer

The method of corners involves finding the corner points of the feasible region and evaluating the objective function at each of them.

The given constraints are: 
2x + y ≤ 10 
x + 2y ≤ 11 
x, y ≥ 0

Solving these equations by graphing or substitution, we can find the corner points: 
(0,0), (0,5.5), (2.5,2.5), and (5.5,0)

Evaluating the objective function at each of these points, we get: 
(0,0): 0 
(0,5.5): 60.5 
(2.5,2.5): 27.5 
(5.5,0): 60.5

The maximum value of the objective function is obtained at (5.5,0), with a value of 60.5. Therefore, the best choice is D, with x=0, y=4, and P=16.

Solve the Linear Programming Problem by the Method of Corners