Solution of Linear Programming Problems

The feasible region in LPP is always

What are conflicting constraints. Show that the LPP in which the objective function $z=6x+4y$ is to be minimized subject to the constraints $3x+2y\ge 18$ and $2x+y\le 16 \left(x\ge 0, y\ge 0\right)$ has infinitely many optimal solutions.

What are conflicting constraints. 

What are conflicting constraints. Show that if each of the infinitely many optimal solutions of an LPP with objective function $z=ax+by$, lies on the line $15 x+25 y=32$ with $5a=3b$.

What are conflicting constraints. Find optimal solution of the following LPP, Maximize $z=2x+3y$ subject to $5x+4y\le 20$, where $x\ge 0, y\ge 0$.

What are conflicting constraints. 

Show that the optimal solution of the following LPP

Maximize $z=5x+3y$

Subject to, $x+2y\le 16$,

$0\le y\le 3$,

$x\ge 0$

lies on the straight line $2x+5y=32$.

Solve $z=2x+3y$, subject to $x+y\le 6$, $2x+y\ge 16$, $x\ge 0$, $y\ge 0$ graphically. Check whether it has feasible or infeasible solution.

Solve $z=3x+2y$, subject to $x+y\le 5$, $2x+y\ge 20$, $x\ge 0$, $y\ge 0$ graphically. Check whether it has feasible or infeasible solution.

Solve $z=2x+2y$, subject to $x+y\le 5$, $x+2y\ge 14$, $x\ge 0$, $y\ge 0$ graphically. Check whether it has feasible or infeasible solution.

Solve $z=x+2y$, subject to $x+y\le 5$, $3x+y\ge 21$, $x\ge 0$, $y\ge 0$ graphically. Check whether it has feasible or infeasible solution.

Solve $z=4x+3y$, subject to $x+y\le 6$, $2x+y\ge 20$, $x\ge 0$, $y\ge 0$ graphically. Check whether it has feasible or infeasible solution.

Check if $z=4x+3y$, subject to $x+y\le 6$, $2x+y\ge 20$, $x\ge 0$, $y\ge 0$ has feasible or infeasible solution graphically.

If $-1\le x\le 2$ and $1\le y\le 3$ then least possible value of $2y-3x$ is

Solution of the LPP Min. $\mathrm{Z}=5x+10y$ subject to: $x+2y\le 120,$ $x+y\ge 60,$ $x-2y\ge 0,$ $x, y\ge 0$ is

The coordinates of the corner points of the bounded feasible region are $(10,0),(2,4),(1,5)$ and $(0,8)$. the maximum of objective function $z=60x+10y$ is$\dots \dots \dots .$

For the following linear programming problem, find the minimum value of $z=8000x+12000y$,  where constraints are 

$3x+4y\le 60$

$x+3y\le 30$

$x⩾0, Y⩾0$

The region of feasible solution under the constraints $2x+y\le 6, x\ge 0, y\ge 0$ is:

Solve the following problem graphically :

Minimise and Maximise

$\mathrm{Z}=3x+9y$

Subject to the constraints :

$x+3y\le 60$

$x+y\ge 10$

$x\le y$

$x\ge 0, y\ge 0$.

For the following linear programming problem:

Objective function: $z=150x+250y$

Subject to: $4x+y\le 40$

$3x+2y\le 60$

$x\ge 0$

$y\ge 0$

The maximum value of $z$ is

For the following linear programming problem.

$x+2y\le 20,$ $3x+2y\le 30, x⩾0, y⩾0$ and $z=20x+30y$.