Consider the LPP: Maximize $z = x + y$ subject to the constraints $x + 2y \leq 70$, $2x + y \leq 95$, $x,y \geq 0$. The optimal feasible solution is

The objective is to maximize $z = x + y$ subject to:

• $x + 2y \leq 70$
• $2x + y \leq 95$
• $x, y \geq 0$

Testing each option against the constraints:

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For $(20, 35)$:

$x + 2y = 20 + 2(35) = 20 + 70 = 90$

Since $90 > 70$, the first constraint is violated.

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For $(35, 20)$:

$x + 2y = 35 + 2(20) = 35 + 40 = 75$

Since $75 > 70$, the first constraint is violated.

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For $(30, 25)$:

$x + 2y = 30 + 2(25) = 30 + 50 = 80$

Since $80 > 70$, the first constraint is violated.

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For $(40, 15)$:

$x + 2y = 40 + 2(15) = 40 + 30 = 70 \leq 70$

$2x + y = 2(40) + 15 = 80 + 15 = 95 \leq 95$

$x = 40 \geq 0$ and $y = 15 \geq 0$

All constraints are satisfied.

$z = x + y = 40 + 15 = 55$

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The optimal feasible solution is $(40, 15)$ with maximum value $z = 55$.