Question

The corner points of the feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5), then the minimum value of z = 4x + 6y occurs at

• A. finite number of points
• B. only one point
• C. infinite number of points
• D. only two points

Answer 1

Answer: (D)

only two points

Answer 2

$z = 4x + 6y$
Let's substitute the coordinates of each corner point into the objective function:
For point $(0, 2): z = 4(0) + 6(2) = 12$
For point $(3, 0): z = 4(3) + 6(0) = 12$
For point $(6, 0): z = 4(6) + 6(0) = 24$
For point $(6, 8): z = 4(6) + 6(8) = 72$
For point $(0, 5): z = 4(0) + 6(5) = 30$
From the evaluations, we can see that the minimum value of z occurs at two points, namely (0, 2) and (3, 0), both having a value of 12.
Therefore, the correct option is (D) only two points.