Consider a LPP:

Maximize $Z=22x+18y$

Subject to:

$x+y\le 20$,

$360x+240y\le 5760$,

$x,y\ge 0$.

Which of the following statements are correct ?

A. The maximum value of $Z$ occurs at (0, 20).

B. The maximum value of $Z$ occurs at (8, 12).

C. The maximum value of $Z$ is 352.

D. The maximum value of $Z$ is 392.

Choose the correct answer from the options given below:

The region represented by the system of inequalities $x, y \geq 0, y \leq 6, x + y \leq 3$

Two linear programming problems (LPPs) have same bounded feasible region with three corner points $(0, 3), (4, 4), (7, 0)$. If $Z_1 = x - 3y$ and $Z_2 = 2x + y$ are objective functions of LPPs, then which of the following is/are correct?

A. only $Z_1$ maximizes at $(7, 0)$.

B. both $Z_1, Z_2$ minimize at $(0, 3)$.

C. both $Z_1, Z_2$ maximize at $(7, 0)$.

D. $Z_2$ maximizes at $(4, 4)$.

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The corner points of the feasible region of the LPP: Minimize $Z = -50x + 20y$ subject to $2x - y \geq -5$, $3x + y \geq 3$, $2x - 3y \leq 12$ and $x, y \geq 0$ are

Consider the objective function $Z = 3x + 4y$ subject to the following constraints: $x-6y \le 6, x+y-1 \ge 0, x-y+1 \ge 0, x+2y \le 6, x \ge 0, y \ge 0$ . Which of the following inequalities does not contribute to the feasible region?

Consider the following L.P.P.

Minimize z = 400x + 300y subject to 100x + 200y ≥ 12000, 300x + 400y ≥ 20000, 200x + 100y ≥ 15000 and x, y ≥ 0. Then

In a LPP, Let R be the feasible region, then which of the following are TRUE?

A. If R is bounded, then the objective function Z has both a maximum and minimum value on R.

B. If R is unbounded, then the objective function Z may or may not have a maximum or minimum value.

C. If a optimal solution exists. It must occur at atleast one corner point of R.

D. If R is bounded, then maximum value will exist but minimum may or may not exist for an objective function Z.

Choose the correct answer from the options given below: