# Which of the  following pairs is the solution to the LP problemmin $\mu_{1}+2\mu_{2}$ 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) $\left ( \mu_{1},\mu_{2} \right )=\left ( 0,7 \right )$

As we learnt in

Corner Point Method -

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

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$z= \mu _{1}+ 2\mu_{2}$

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

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

$\mu_{1} \geq 0$

$\mu_{2} \geq 0$

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

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