Let x and y be optimal solution of an LP problem, then ...... - Vidyadip

MCQ

Let $x$ and $y$ be optimal solution of an $LP$ problem, then $......$

A
$z=\lambda x+(1-\lambda) y, \lambda \in \mathrm{R}$ is also an optimal solution
✓
$z=\lambda x+(1-\lambda) y, 0 \leq \lambda \leq 1$ gives an optimal solution.
C
$z=\lambda x+(1+\lambda) y, 0 \leq \lambda \leq 1$ gives an optimal solution.
D
$z=\lambda x+(1+\lambda) y, \lambda \in \mathrm{R}$ gives an optimal solution.

✓

Answer

Correct option: B.

$z=\lambda x+(1-\lambda) y, 0 \leq \lambda \leq 1$ gives an optimal solution.

b
for $L P$

If $x, y$ are optind solutions

So a multiple of $z=\lambda x+(1-\lambda) y, \lambda \in R$ is abo an optimal sivhin

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If ${t_n} = \frac{1}{4}(n + 2)\,(n + 3)$ for $n = 1, 2, 3,……$ then $\frac{1}{{{t_1}}} + \frac{1}{{{t_2}}} + \frac{1}{{{t_3}}} + .... + \frac{1}{{{t_{2003}}}} = $

If the odds in favour of an event be $3 : 5$, then the probability of non-occurrence of the event is

Statement $-1 :$Determinant of a skew-symmetric matrix of order $3$ is zero

Statement $-2 :$ For any matrix $A,$ $\det \left( {{A^T}} \right) = {\rm{det}}\left( A \right)$ and $\det \left( { - A} \right) = - {\rm{det}}\left( A \right)$ Where $\det \left( A \right) = A$. Then :

How many words can be made from the letters of the word $INSURANCE$, if all vowels come together

If $\int {({x^3} - 2{x^2} + 5){e^{3x}}\,dx} \,$ $= e^{3x} (Ax^3 + Bx^2 + Cx + D)$ then the statement which is incorrect is

Let in equilateral $\Delta ABC,$ $A(-1 + acos \theta, 2 + asin \theta), B(-1 + acos \alpha, 2 -asin \alpha), C(-1 + asin \beta, 2 + acos \beta)$ and length of median through vertex $A$ is $2b,$ then equation of circumcircle of triangle $ABC$ is (where a is consant) -

If three conterminous edges of a parallelopiped are represented by $a - b,\,\,b - c$ and $c - a$, then its volume is

If $a, b, c$ are mutually perpendicular vectors of equal magnitudes, then the angle between the vectors $a$ and $a + b + c$ is

Let the set of all positive values of $\lambda$, for which the point of local minimum of the function $\left(1+x\left(\lambda^2-x^2\right)\right)$ satisfies $\frac{x^2+x+2}{x^2+5 x+6}<0$, be $(\alpha, \beta)$. Then $\alpha^2+\beta^2$ is equal to........

If the system of linear equations $2 x + y - z =7$ ; $x-3 y+2 z=1$ ; $x +4 y +\delta z = k$, where $\delta, k \in R$ has infinitely many solutions, then $\delta+ k$ is equal to