Solution of Linear Programming Problems

Which one of the following is infeasible solution to the linear programming problem (LPP), whose feasible region is given by:

A company produces two types of goods, $A$ and $B$, that require gold and silver. Each unit of type $A$ requires $3 \mathrm{g}$ of silver and $1 \mathrm{g}$ of gold, while that of type $B$ requires $1 \mathrm{g}$ of silver and $2 \mathrm{g}$ of gold. The company can use at the most $9 \mathrm{g}$ of silver and $8 \mathrm{g}$ of gold. If each unit of type $A$ brings a profit of $₹ 40$  and that of type $B$ $₹ 50$, find the number of units of each type that the company should produce to maximize the profit. Formulate and solve graphically the LPP and find the maximum profit.

An infeasible solution would occur when:

An iso-profit line represents:

Define convex set.

What is meant by convex set?

Find the vertices of feasible region.

$x+3y\ge 3$, $x+y\ge 2$ and $x, y\ge 0$

Find the vertices of feasible region.

$x+2y\le 8$, $3x+2y\le 12$ and $x, y\ge 0$

Solve the following $\mathrm{LPP}$

Min $Z=3x+5y$

$x+3y\ge 3$

$x+y\ge 2$

$x, y\ge 0$

Solve the following $\mathrm{LPP}$.

Max $Z=6x+4y$

Subject to $x\le 2$

$x+y\le 3$

$-2x+y\le 1$

$x, y\ge 0$

Solve the following $\mathrm{LPP}$.

Max $Z=4x+3y$

$x+2y\le 8$

$3x+2y\le 12$

$x, y\ge 0$

Unbounded feasible region will have both maximum value or minimum value for the objective function of a linear programming problem.

Define unbounded feasible region in linear programming.

If the feasible region of a linear programming problem can be circumscribed, then it is called unbounded feasible region.

Define bounded feasible region.

Define feasible region in linear programming problem.

State the Convex polygon theorem.

Find convex region from the following figures.

The corner points of the feasible region determined by the following system of linear inequalities:
$2x+y\le 10,x+3y\le 15,x,y\ge 0$ are $\left(0,0\right),\left(5,0\right),\left(3,4\right)$ and $\left(0,5\right)$
Let $Z=px+qy,$ where $p,q>0.$
Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both $\left(3,4\right)$ and $\left(5,0\right)$ is

The bounded feasible region for a linear programming problem (LPP) is given as below:

Which one of the following can be optimal solution for the given LPP.

Which one of the following is infeasible solution to the linear programming problem (LPP), whose feasible region is given by:

Find the maximum value of $Z=3x+4y$ subject to constraints $x+y\le 4, x\ge 0, y\ge 0$.