Find the minimum value of $\mathrm{Z}=3 \mathrm{x}+5 \mathrm{y}$, subject to the constraints $-2 \mathrm{x}+\mathrm{y} \leq$ $4, \mathrm{x}+\mathrm{y} \geq 3, \mathrm{x}-2 \mathrm{y} \leq 2, \mathrm{x} \geq 0$ and $\mathrm{y} \geq 0$ $Z=3 x+5 y$, subject to the constraints $-2 x+y \leq 4, x+y \geq 3, x-2 y \leq 2, x \geq 0$ and $y \geq 0$

Find the minimum value of $\mathrm{Z}=3 \mathrm{x}+5 \mathrm{y}$ , subject to the constraints $-2 \mathrm{x}+\mathrm{y} \leq$ $4, \mathrm{x}+\mathrm{y} \geq 3, \mathrm{x}-2 \mathrm{y} \leq 2, \mathrm{x} \geq 0$ and $\mathrm{y} \geq 0$ $Z=3 x+5 y$ , subject to the constraints $-2 x+y \leq 4, x+y \geq 3, x-2 y \leq 2, x \geq 0$ and $y \geq 0$

Maths | Previous Year Question Papers

$Z=3 x+5 y$ , subject to the constraints
$-2 x+y \leq 4, x+y \geq 3, x-2 y \leq 2, x \geq 0$ and $y \geq 0$
Draw the line $-2 x+y=4, x+y=3$ and $x-2 y=2$ and shaded region which is satisfied by above inequalities
We know that the feasible region is bounded
$A(8 / 3,1 / 3), B(0,3)$ and $C(0,4)$ are the corner points
Value of $Z$ at $A(8 / 3,1 / 3)$

$Z=3 \times 8 / 3+5 \times 1 / 3=29 / 3=92 / 3$

Value of $Z$ at $B(0,3)$

$Z=3 \times 0+5 \times 3=15$

Value of $\mathrm{Z}$ at $\mathrm{C}(0,4)$
Hence, the maximum value of $Z$ is $92 / 3$ which occurs at $A(8 / 3,1 / 3)$ .

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