Linear Programming

"A storage room must be kept at a temperature (T) such that triple the temperature is at least $\mathbf{1 5}^{\circ} \mathbf{C}$, but the temperature plus $\mathbf{8}$ is strictly not more than $\mathbf{2 0}^{\circ} \mathbf{C}$. What is the...

Which of the following is NOT a comer point of the feasible region determined by the constraints:
$$ \begin{aligned} & x+2 y \leq 4 \\ & x+y \geq 2 \\ & x \geq 0 \text { and } y \geq 0 \end{aligned} $$

The feasible region represented by the constraints:
$$ \begin{aligned} & x+2 y \leq 120 \\ & x+y \geq 60 \\ & x-2 y \geq 0 \\ & x \geq 0 \text { and } y \geq 0 \end{aligned} $$

For a given Linear Programming problem, the objective function is
\(z=3 x+2 y\)
Subject to constraints are
$$\begin{aligned} & 4 x+3 y \leq 60 \\ & x \geq 3 \\ & y \leq 2 x \\ & y \geq 0 \end{aligned}$$
P is one of the corner points of the ...

The solution for the following system of inequalities $3 x-7<5+x$ and $11-5 x \leq 1$ on a real number line is

Given $Z=80 x+120 y$, subject to constraints are $x+3 y \leq 30 ; 3 x+4 y \leq 60 ; x \geq 0 ; y \geq 0$.
P is one of the corner points of the feasible region for the given Linear Programming Problem.
Then the coordinate of $P$ is

The corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0)$, If objective function is $Z=p x+q y, p, q>0$ then the condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3,0...

The minimum value of \(Z=150 x+200 y\) for the given constraints
$$\begin{aligned} & 3 x+5 y \geq 30 \\ & x+y \geq 8 ; x \geq 0, y \geq 0 \text { is } \end{aligned}$$

The maximum value of \(P=500 x+400 y\) for the given constraints \(x+y \leq 200, \quad x \geq 20, \quad y \geq 4 x, \quad y \geq 0\) is

\(\text { The maximum value of } Z=3 x+4 y \text { for the given constraints } x+2 y \leq 76,2 x+y \leq 104, x \geq 0, y \geq 0 \text { is }\)

The minimum value of \(Z=3 x+5 y\), given subject to the constraints \(x+y \geq 2, x+3 y \geq 3, x, y \geq 0\) is

The maximum value of \(Z=12 x+13 y\), subject to constraints \(x \geq 0, y \geq 0, x+y \leq 5\) and \(3 x+y \leq 9\) is

The maximum value of \(Z=10 x+16 y\), subject to constraints \(x \geq 0, y \geq 0, x+y \leq 12,2 x+y \leq 20\) is

The feasible region for the inequations \(x+2 y \geq 4,2 x+y \leq 6, x, y \geq 0\) is

Maximum value of \(z=12x+3y\), subject to constraints \(x\ge0,y\ge0,x+y\ge5\) and \(3x+y\le9\) is

The maximum of Z is where, \(Z=4x+2y\) subject to constraints \(4x+2y\ge46,x+3y\le24\) and \(x,y\ge0\) is

Shade the feasible region for the inequations \(6x+4y\le120, 3x+10y\le180,x,y\ge0\) in a rough figure.

Write the solution of the following LPP
Maximize \(Z=x+y\)
Subject to \(3x+4y\le12,x\ge0,y\ge0\).
Which point the value of Z is maximum?

The maximum value of \(x+y\) subject to \(2x+3y\le6,x\ge0,y\ge0\) is

Shade the feasible region for the inequations \(x+y\ge2,2x+3y\le6,x\ge0,y\ge0\) in a rough figure.