For the constriants $x + y \le 60$, $5x + y \le 100$ and $x \ge 0, y \ge 0$, the feasible region is:

If $5x + y \leq 100$, $x + y \leq 60$, $x \geq 0$, $y \geq 0$. Then one of the corner points of the feasible region is :

Max (z) = 5x + 10y subject to constraints:

$x + 2y < 120$

$x + y > 60$

$x - 2y > 0$

$x, y \geq 0$

Which of the following points do not lie in the feasible region of the above LPP ?

(A) (90, 15)

(B) (30, 15)

(C) (60, 20)

(D) (90, 10)

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Consider the LPP: Maximize $z = x + y$ subject to the constraints $x + 2y \leq 70$, $2x + y \leq 95$, $x,y \geq 0$. The optimal feasible solution is

The corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 3/2), (1, 2) and (4, 0). If the objective function is Z = ax + by, where 'a' and 'b' are positive, then the condition on 'a' and 'b' so that the maximum of Z occurs at (1, 2) and (4, 0) is:

Let the corner points of the bounded feasible region of an LPP determined by a set of constraints are A(1, 5), B(3, 2) and C(2, 1). If the objective function $z=2ax+by$, $a,b>0$ has maximum values at points A and B, and z has minimum value 8 at point C, then the value of $4a+b$ is:

If the corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 2), (3, 0), (6, 0), (6, 8) and (0,5), then which of the following are correct for the objective function $Z = 4x + 6y$?

(A) The minimum value of the objective function occurs at (0, 2) and (3, 0) only.

(B) The minimum value of the objective function occurs at the mid-point of the line segment joining the points (0, 2) and (3, 0) only.

(C) The minimum value of the objective function occurs at every point of the line segment joining the points (0, 2) and (3, 0).

(D) The difference between the maximum value and minimum value of the objective function is 60.

Choose the correct answer from the options given below: