If $z = 3x + 4y$ be the objective function of a of a linear programming problem (LPP) and (3, 1), (2, 4), (0, 4), (5, 0) be corner points of the bounded feasible region. Then the maximum value of objective function is

A person wants to invest an amount of ₹ $75,000$. He has two options A and B yielding $8 \%$ and $9 \%$ return respectively on the invested amount. He plans to invest at least ₹ $15,000$ in Plan A and at least ₹ $25,000$ in Plan B. Also he wants that his investment in Plan A is less than or equal to his investment in Plan B. Which of the following options describes the given LPP to maximize the return (where $x$ and $y$ are investments in Plan A and Plan B respectively) ?

The corner points of a bounded feasible region are $A(15,0), B(40,0), C(4,18)$ and $D(6,12)$. If the objective function is $z = 20x + 10y$, then the difference in maximum and minimum value of $z$ is

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s):

The optimal solution of the Linear Programming problem

Maximize $Z = 3x_1 + 5x_2$,

s.t. $3x_1 + 2x_2 \leq 18$

$x_1 \leq 4$

$x_2 \leq 6$

$x_1 \geq 0, x_2 \geq 0$ is

The feasible region and optimal solution of a LPP with objective function, max.$(z) = 600x + 400y$, subject to :

$x + 2y \leq 12$, $2x + y \leq 12$, $x + 1.25y \geq 5$, $x \geq 0$ and $y \geq 0$, is:

The feasible region and optimal solution is _____

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.

Choose the correct answer from the options given below: