If x+y 2, x 0, y 0 the point at which maximum value of 3x + 2y at… - Vidyadip

MCQ

If $\text{x}+\text{y}\leq2,$ $\text{x}\leq0,$ $\text{y}\leq0$ the point at which maximum value of 3x + 2y attained will be.

✓
$(0,0)$
B
$\Big(\frac{1}{2},\frac{1}{2}\Big)$
C
$(0,2)$
D
$(2,0)$

✓

Answer

Correct option: A.

$(0,0)$

$\text{x}\leq0$ and $\text{y}\leq0$ represents third Quadrant $\text{x}+\text{y}\leq2$ represents the region below the line $\text{x}+\text{y}\leq2$ (the region which contains origin)
The common region of given set of equations is third quadrant (including negative x axis and negative y axis)
Since x and y values are $\leq0$ in the third quadrant, the maximum value of 3x + 2y occurs at x = 0 and y = 0 and the maximum value is 0.

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