Question 2 :
A dealer wishes to purchase toys $A$ and $B$. He has Rs. $580$ and has space to store $40$ items. $A$ costs Rs. $75$ and $B$ costs Rs. $90$. He can make profit of Rs. $10$ and Rs.$15$ by selling $A$ and $B$ respectively assuming that he can sell all the items that he can buy formulation of this as L.P.P. is

Question 3 :
In order for a linear programming problem to have a unique solution, the solution must exist

Question 4 :
Linear programming model which involves funds allocation of limited investment is classified as

Question 5 :
Consider the objective function $Z = 40x + 50y$ The minimum number of constraints that are required to maximize $Z$ are

Question 6 :
To write the dual; it should be ensured that&#160;&#160;<br/>I. All the primal variables are non-negative.<br/>II. All the bi values are non-negative.<br/>III.&#160;All the constraints are $&#8804;$ type if it is maximization problem and $&#8805;$ type if it is a minimization problem.

Question 7 :
How many acres of each (wheat and rye) should the farmer plant in order to get maximum profit?

Question 8 :
$\displaystyle z=10x+25y$ subject to$\displaystyle 0\le x\le 3$ and$\displaystyle 0\le y\le 3,x+y\le 5$ then the maximum value of z is<br>

Question 9 :
The objective function of LPP defined over the convex set attains its optimum value at

Question 10 :
In order to obtain maximum profit, the quantity of normal and scientific calculators to be manufactured daily is:

Question 15 :
The corner points of the feasible region determined by the system of linear constraints are $(0, 10), (5, 5), (15, 15), (0, 20)$. Let $z=px+qy$ where $p, q &gt; 0$. Condition on p and q so that the maximum of z occurs at both the points $(15, 15)$ and $(0, 20)$ is __________.

Question 16 :
Choose the most correct of the following statements relating to primal-dual linear programming problems:

Question 17 :
In linear programming, oil companies used to implement resources available is classified as

Question 18 :
An article manufactured by a company consists of two parts $X$ and $Y$. In the process of manufacture of the part $X$. $9$ out of $100$ parts may be defective. Similarly $5$ out of $100$ are likely to be defective in part $Y$. Calculate the probability that the assembled product will not be defective.

Question 19 :
The Convex Polygon Theorem states that the optimum (maximum or minimum) solution of a LPP is attained at atleastone of the ______ of the convex set over which the solution is feasible.

Question 20 :
Corner points of the bounded feasible region for an LP problem are $A(0,5) B(0,3) C(1,0) D(6,0)$. Let $z = -50x + 20y$ be the objective function. Minimum value of z occurs at ______ center point.

Question 21 :
For a linear programming equations, convex set of equations is included in region of

Question 23 :
The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.<br/><table class="table table-bordered"><tbody><tr><td rowspan="2">&#160;<b>Colour</b></td><td colspan="3"><b>&#160; &#160;Number of cars manufactured</b></td></tr><tr><td><b>&#160;Vento</b></td><td><b>&#160;Creta</b></td><td><b>WagonR&#160;</b></td></tr><tr><td>&#160;Red</td><td>&#160;65</td><td>&#160;88</td><td>&#160;93</td></tr><tr><td>&#160;White</td><td>&#160;54</td><td>&#160;42</td><td>&#160;80</td></tr><tr><td>&#160;Black</td><td>&#160;66</td><td>&#160;52</td><td>&#160;88</td></tr><tr><td>&#160;Sliver</td><td>37</td><td>&#160;49</td><td>&#160;74</td></tr></tbody></table>Which car was twice the number of silver Vento?

Question 24 :
Vikas printing company takes fee of Rs. $28$ to print a oversized poster and Rs. $7$ for each colour of ink used. Raaj printing company does the same work and charges poster for Rs. $34$ and Rs. $5.50$ for each colour of ink used. If $z$ is the colours of ink used, find the values of $z$ such that Vikas printing company would charge more to print a poster than Raaj printing company.<br/><br/>

Question 25 :
If $a,b,c \in +R$ such that $\lambda abc$ is the minimum value of $a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2)$, then $\lambda=$

Question 26 :
The corner points of the feasible region are $A(0,0),B(16,0),C(8,16)$ and $D(0,24)$. The minimum value of the objective function $z=300x+190y$ is _______

Question 28 :
In transportation models designed in linear programming, points of demand is classified as

Question 29 :
The number of constraints allowed in a linear program is which of the following?

Question 30 :
In Graphical solution the feasible solution is any solution to a LPP which satisfies

Question 31 :
Which of the following statements about an LP problem and its dual is false?

Question 32 :
<p>In graphical solutions of linear inequalities, solution can be divided into</p><ol></ol>

Question 33 :
Given a system of inequation:$\displaystyle 2y-x\le 4$<br/>$\displaystyle -2x+y\ge -4$Find the value of $s$, which is the greatest possible sum of the $x$ and $y$ co-ordinates of the point which satisfies the following inequalities as graphed in the $xy$ plane.<br/>

Question 36 :
While plotting constraints on a graph paper, terminal points on both the axes are connected by&#160;a straight line because:

Question 38 :
For the LPP; maximise $z=x+4y$ subject to the constraints $x+2y\leq 2$, $x+2y\geq 8$, $x, y\geq 0$.

Question 39 :
In order to maximize the profit of the company, the optimal solution of which of the following equations is required?

Question 41 :
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?

Question 42 :
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.

Question 43 :
If two constraints do not intersect in the positive quadrant of the graph, then

Question 44 :
Minimise $Z=\sum _{ j=1 }^{ n }{ \sum _{ i=1 }^{ m }{ { c }_{ ij }.{ x }_{ ij } } } $<br>Subject to $\sum _{ i=1 }^{ m }{ { x }_{ ij } } ={ b }_{ j },j=1,2,......n$<br>$\sum _{ j=1 }^{ n }{ { x }_{ ij } } ={ b }_{ j },j=1,2,......,m$ is a LPP with number of constraints

Question 46 :
Which of the following is a property of all linear programming problems?

Question 47 :
If $x$ is any real number, then which of the following is correct?

Question 49 :
An objective function in a linear program can be which of the following?<br>