" the relation S is defined on $N\times N\left ( a,b \right )S\left ( c,d \right )\Leftrightarrow bc\left ( a+d \right )=ad$ in an equivalance " that statement is ?

If a = b then ax = ...........

If  x + y = 3 and xy = 2, then the value of $\displaystyle x^{3}-y^{3}$ is equal to 

What is the solution of $x\le 4,y\ge 0$ and $x\le -4,y\le 0$ ?

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that

If the constraints in linear programming problem are changed

A wholesale merchant wants to start the business of cereal with Rs. $24000$. Wheat is Rs. $400$ per quintal and rice is Rs. $600$ per quintal. He has capacity to store $200$ quintal cereal. He earns the profit Rs.$25$ per quintal on wheat and Rs. $40$ per quintal on rice. If he stores $x$ quintal rice and $y$ quintal wheat, then for maximum profit the objective function is

The feasible solution of an LP problem, is ________

The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.

Let $P(-1, 0), Q(0, 0)$ and $R(3, 3\sqrt{3})$ be three points. The equation of the bisector of the angle PQR is?

Maximum value of $z = 6 x + 11 y$ ,  subject to $2 x + y \leq 104 , x + 2 y \leq 76 , x \geq 0 , y \geq 0$ is

The taxi fare in a city is as follows. For the first km the fare is $Rs.10$ and subsequent distance is $Rs.6 / km.$ Taking the distance covered as $x \ km$ and fare as $Rs\ y$ ,write a linear equation.

The problem associated with  $ LPP$  is

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

Linear programming used to optimize mathematical procedure and is

In linear programming, oil companies used to implement resources available is classified as

Linear programming model which involves funds allocation of limited investment is classified as

Which of the following is a property of all linear programming problems?

In transportation models designed in linear programming, points of demand is classified as

Consider the following linear programming problem:

Which of the following points $(X,Y)$ could be a feasible corner point?

Consider the following linear programming problem:

Which of the following points $(X,Y)$ is feasible?

Unboundedness is usually a sign that the LP problem.

The first step in formulating an LP problem is

Consider the following linear programming problem:

Which of the following points $(X,Y)$ is in the feasible region?

In order for a linear programming problem to have a unique solution, the solution must exist

Consider the following linear programming problem:

Which of the following points $(X,Y)$ is feasible?

Which of the following statements about an LP problem and its dual is false?

Mark the wrong statement:

In linear programming context, sensitivity analysis is a technique to

Choose the wrong statement:

The number of constraints allowed in a linear program is which of the following?

Which of the following is an essential condition in a situation for linear programming to be useful?

Choose the most correct of the following statements relating to primal-dual linear programming problems:

Apply linear programming to this problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is $100 and the profit in the manufacture of a unit of product E is $87. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,000. Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?

To write the dual; it should be ensured that  
I. All the primal variables are non-negative.
II. All the bi values are non-negative.
III. All the constraints are $≤$ type if it is maximization problem and $≥$ type if it is a minimization problem.

If $x=\log _{2^2}2+\log _{2^3}2^2+\log _{2^4}2^3......+\log _{2^{n+1}}2^n+$, then the minimum value of $x$ will be-

If $a,b >0$, $a+b=1$, then the least value of $(1+\dfrac 1a)(1+\dfrac 1b)$, is

If $l,m,n$ be three positive roots of the equation $x^3-ax^2+bx+48=0$, then the minimum value of $\dfrac 1l +\dfrac 2m+\dfrac 3n$ is

Let $a _1,a _2....,a _n$ be a non negative real number such that $a _1+a _2....+a _n=m$ and let $S=\underset{i<j}\sum a _ia _j$, then

A firm manufactures three products $A,B$ and $C$. Time to manufacture product $A$ is twice that for $B$ and thrice that for $C$ and if the entire labour is engaged in making product $A,1600$ units of this product can be produced.These products are to be produced in the ratio $3:4:5.$ There is demand for at least $300,250$ and $200$ units of products $A,B$ and $C$ and the profit earned per unit is Rs.$90,$ Rs$40$ and Rs.$30$ respectively.

Formulate the problem as a linear programming problem and find all the constraints for the above product mix problem.

Find the output of the program given below if$ x = 48$
and $y = 60$
10  $ READ x, y$
20  $Let x = x/3$
30  $ Let y = x + y + 8$
40  $ z = \dfrac y4$
50  $PRINT z$
60  $End$

For any positive real number $a$ and for any $n \in N$, the greatest value of 
$\dfrac {a^n}{1+a+a^2....a^{2n}}$ is

The rod of fixed length $k$ slides along the coordinate axes. If it meets the axes at $A(a,0)$ and $B(0,b)$, then the minimum value of $\left(a+\dfrac 1a\right) ^2+\left(b+\dfrac 1b\right) ^2$ is

If $a>0$, then least value of $(a^3+a^2+a+1) ^2$ is