Use graphical methods to solve the linear programming problem.
-
A) Minimum of 0 when x = 0 and y = 0
B) Minimum of 20 when x = 10 and y = 0
C) Minimum of 20 when x = 2 and y = 4
D) Minimum of 20 when x = 2 and y = 4, as well as when x = 10 and y = 0, and all points in between

Question

Use graphical methods to solve the linear programming problem.
-
A) Minimum of 0 when x = 0 and y = 0 
B) Minimum of 20 when x = 10 and y = 0 
C) Minimum of 20 when x = 2 and y = 4 
D) Minimum of 20 when x = 2 and y = 4, as well as when x = 10 and y = 0, and all points in between

Quizplus · Accepted Answer

The solution space is the shaded area in the graph. The optimal solution lies at the corner points of the feasible region. The objective function line (y = 40-2x) is shown in green. The line intersects with the feasible region at two corner points, (2,4) and (10,0), both yielding a minimum value of 20. Therefore, the best choice is D which includes both optimal solutions.

![linear programming graph](https://i.imgur.com/NEMyBV8.png) The graphical solution shows that the feasible region is a triangle with vertices at (0,0), (10,0), and (2,4). The objective function, 3x + 4y, is a straight line, shown in red on the graph. The minimum value occurs where this line is tangent to the feasible region, which is at the two vertices that form the segment connecting (0,0) and (2,4), as well as all points in between. Therefore, the minimum value is achieved at x = 2 and y = 4, as well as when x = 10 and y = 0, and all points in between.

Use Graphical Methods to Solve the Linear Programming Problem