If corner points of a feasible region are (0, 0), (2, 0), $\left(\frac{20}{19}, \frac{45}{19}\right)$ and (0, 3), then

(A) Maximum value of $z = 5x + 3y$ is 10

(B) Minimum value of $z = 5x + 3y$ is 0

(C) Maximum value of $z = 5x + 3y$ is $\frac{235}{19}$ and minimum value is 0

(D) Maximum value of $z = 5x + 3y$ is 10 and minimum value is 0

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Owner of a whole sale computers shop plans to sell 2 types of computers. A desktop and portable model. If $x$ is the number of desktops and $y$ is the number of portable model and the shop's capacity cannot exceed 250 units. Which of the following is correct ?

Which of the following statements are correct in reference to the linear programming problem(LPP):

Maximize ${Z} = 5x + 2y$

subject to the following constraints

$3x + 5y \leq 15$, $5x + 2y \leq 10$, $x \geq 0, y \geq 0$.

(A) The LPP has a unique optimal solution at $(2, 0)$ only.

(B) The feasible region is bounded with corner points $(0, 0)$, $(2, 0)$, $(20/19, 45/19)$ and $(0, 3)$.

(C) The optimal value is unique, but there are an infinite number of optimal solutions.

(D) The feasible region is unbounded.

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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.

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The corner points of the bounded feasible region for an L.P.P are (0, 10), (5, 5), (15,15), and (0, 20). If the objective function is $Z=px+qy, p,q>0$, then the condition on $p$ and $q$ so that the maximum of $Z$ occurs at (15, 15) and (0, 20) is

If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and $z = px + qy$, $(p,q > 0)$ is an objective function. Then the relation between $p$ and $q$, when $z$ is maximum at $D(4,10)$ and $C(6,8)$, is:

Consider an LPP:

Maximize $Z = 5x + y$

Subject to $x + 3y \le 12$

$3x + y \le 12$

and $x,y \ge 0$

then which of the following statements are TRUE ?

A. The corner points of the bounded feasible region are (0,0), (4,0), (3,3) and (0,4).

B. Maximum value of $z$ occurs at (3,3).

C. Maximum value of $z$ occurs at (4,0).

D. The maximum value of $z$ is 20.

Choose the correct answer from the options given below: