If the points (5, 5, 5) and (7, 9, 5) are both optimal solutions to a linear programming problem, what other point is also optimal?
A)(6,7,8)
B)(6,7,5)
C)(7,5,5)
D)(5,9,5)

Question

Quizplus · Accepted Answer

In linear programming, if two points are optimal solutions, then any point on the line segment connecting these two points is also an optimal solution. The points (5, 5, 5) and (7, 9, 5) form a line segment in 3D space, and the point (6, 7, 5) lies exactly between them, maintaining the same z-coordinate and averaging the x and y coordinates. This makes it also an optimal solution due to the convexity of the solution set in linear programming.

If the Points (5, 5, 5) and (7, 9, 5)