Solve the linear programming problem by the method of corners. Maximize subject to
A) x = 25; y = 5; P = 105
B) x = 0; y = 25; P = 105
C) x = 10; y = 5; P = 30
D) x = 25; y = 5; P = -100
E) x = 0; y = 25; P = -100

Question

Solve the linear programming problem by the method of corners. Maximize  subject to    
A) x = 25; y = 5; P = 105 
B) x = 0; y = 25; P = 105 
C) x = 10; y = 5; P = 30 
D) x = 25; y = 5; P = -100 
E) x = 0; y = 25; P = -100

Quizplus · Accepted Answer

First, we graph the constraints:

Constraint 1: 2x + y ≤ 60
x-intercept: 30; y-intercept: 60
Plotting these points, we can draw the line and shade the area below it.

Constraint 2: x + 3y ≤ 150
x-intercept: 150; y-intercept: 50
Plotting these points, we can draw the line and shade the area below it.

Constraint 3: x ≤ 25
This is a vertical line at x = 25. We shade to the left of the line to represent x values less than or equal to 25.

Constraint 4: y ≤ 25
This is a horizontal line at y = 25. We shade below the line to represent y values less than or equal to 25.

Next, we identify the corners of the feasible region, which are the points where the lines intersect. The three corners are (0, 25), (25, 5), and (10, 5).

We evaluate the objective function at each corner:
(0, 25): 11(0)(25) = 0
(25, 5): 11(25)(5) = 1375
(10, 5): 11(10)(5) = 550

The maximum value is achieved at (25, 5), with a value of 1375. Therefore, the best choice is A.

Solve the Linear Programming Problem by the Method of Corners