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. Minimum of $Z$ occurs at $....$

A
$(0,0)$
✓
$(0,8)$
C
$(5,0)$
D
$(4,10)$

✓

Answer

Correct option: B.

$(0,8)$

b
$(B) \,\,(0,8)$

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 )

Minimum value of the objective function is $-32$

$\therefore$ Minimum value exists at point $(0,8).$

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