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  • I have a doubt, kindly clarify. - Linear Programming - BITSAT-2

Which of the  following pairs is the solution to the LP problem

min \mu_{1}+2\mu_{2} subject to

3\mu_{1}+\mu_{2}\geq 17,\mu_{1}+4\mu_{2}\geq 16,\mu_{1},\mu_{2}\geq 0

  • Option 1)

    \left ( \mu_{1},\mu_{2} \right )=\left ( 1,4 \right )

  • Option 2)

    \left ( \mu_{1},\mu_{2} \right )=\left ( 2,1\right )

  • Option 3)

    \left ( \mu_{1},\mu_{2} \right )=\left (6,10\right )

  • Option 4)

    \left ( \mu_{1},\mu_{2} \right )=\left ( 0,7 \right )

 

Answers (1)

As we learnt in 

Corner Point Method -

This method of solving a LPP graphically is based on the principle of extreme points theorem.

-

 z= \mu _{1}+ 2\mu_{2}

3\mu_{1}+\mu_{2}\geqslant 17

\mu_{1}+4\mu_{2}\geqslant 16

\mu_{1} \geq 0

\mu_{2} \geq 0

at (1, 4), z= g

(2, 1), z= 4

(6, 10), z= not \ \ taken

min at (2, 1).

 


Option 1)

\left ( \mu_{1},\mu_{2} \right )=\left ( 1,4 \right )

Incorrect

Option 2)

\left ( \mu_{1},\mu_{2} \right )=\left ( 2,1\right )

correct

Option 3)

\left ( \mu_{1},\mu_{2} \right )=\left (6,10\right )

Incorrect

Option 4)

\left ( \mu_{1},\mu_{2} \right )=\left ( 0,7 \right )

Incorrect

Posted by

Vakul

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