The feasible solution for a LPP is shown in Figure Let z=3 x-4 y … - Vidyadip

MCQ

The feasible solution for a LPP is shown in Figure Let $z=3 x-4 y$ be the objective function. (Maximum value of $z+$ Minimum value of $z$ ) is equal to $....$

A
$13$
B
$01$
C
$-13$
✓
$-17$

✓

Answer

Correct option: D.

$-17$

d

Corner point	Objective function $z=3 x-4 y$
$(0,0)$	$z=3(0)-4(0)=0$
$(5,0)$	$z=3(5)-4(0)=15$ (Maximum value)
$(6,5)$	$z=3(6)-4(5)=18-20=-2$
$(6,8)$	$z=3(6)-4(8)=-14$
$(4,10)$	$z=3(4)-4(10)=-28$
$(0,8)$	$z=3(0)-4(8)=-32($ minimum value )

we have (Maximum value of $z$ ) $+$ (Minimum value of $z$ ) $=15-32=-17$.

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