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

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

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

Testing each option against the constraints:

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For $(20, 35)$(20,35):

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

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

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For $(35, 20)$(35,20):

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

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

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For $(30, 25)$(30,25):

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

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

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For $(40, 15)$(40,15):

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

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

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

All constraints are satisfied.

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

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