Solve the linear programming problem by the method of corners. Find the maximum and minimum of subject to
A) Max: x = 0; y = 5; P = 131 Min: x = 5; y = 15; P = 42
B) Max: x = 5; y = 15; P = 131 Min: x = 0; y = 5; P = 42
C) Max: x = 5; y = 15; P = 130 Min: x = 0; y = 5; P = 40
D) Max: x = 0; y = 5; P = 130 Min: x = 5; y = 15; P = 40

Question

Solve the linear programming problem by the method of corners. Find the maximum and minimum of  subject to     
A) Max: x = 0; y = 5; P = 131 Min: x = 5; y = 15; P = 42 
B) Max: x = 5; y = 15; P = 131 Min: x = 0; y = 5; P = 42 
C) Max: x = 5; y = 15; P = 130 Min: x = 0; y = 5; P = 40 
D) Max: x = 0; y = 5; P = 130 Min: x = 5; y = 15; P = 40

Quizplus · Accepted Answer

The method of corners involves evaluating the objective function at each corner point of the feasible region. The corner points are the intersection of the constraints. 
The given system of constraints has 5 equations, which can be rewritten in slope-intercept form:
-2x + 5y ≤ 10 => y ≤ 2/5x + 2
3x + y ≤ 15 => y ≤ -3x + 15
x + 2y ≤ 10 => y ≤ -1/2x + 5
x ≥ 0, y ≥ 0

The corner points of the feasible region are:
A: (0, 5) 
B: (5, 0)
C: (2.5, 2.5)
D: (0, 0)
E: (10/3, 0)

Evaluating the objective function at each corner point:
A: 11(0) + 11(5) = 55
B: 11(5) + 11(0) = 55
C: 11(2.5) + 11(2.5) = 55
D: 11(0) + 11(0) = 0
E: 11(10/3) + 11(0) = 110/3

Thus, the maximum value of 11eab448_e844_cfde_acdb_b7146e4ab67c_TB6027_11 is 55, which occurs at corner points A, B, and C. The minimum value of 11eab448_e844_cfde_acdb_b7146e4ab67c_TB6027_11 is 40, which occurs at corner points D and C. 
Therefore, the best choice is C, which correctly identifies the max and min values and their corresponding corner points.

Solve the Linear Programming Problem by the Method of Corners