Question

solve graphically: max z=4x1+4x2. subject to:x1+2x3<=10;6x1+6x2<=36;x1<6;x1,x2>=0​

Answer 1

Given : x1+2x2<=10;6x1+6x2<=36;x1<6;x1,x2>=0​

To Find : max z=4x1+4x2.

Solution:

x₁ + 2x₂  ≤  10

6x₁ + 6x₂  ≤  36  =>  x₁ +  x₂  ≤  6

x₁  < 6

x₁   ≥ 0

x₂  ≥ 0

x₁ + 2x₂  ≤  10

x₁ +  x₂  ≤  6

=>  x₂ = 4  x₁  = 2

(x₁ , x₂)  = ( 2 , 4)  , ( 6 , 0) , ( 0 , 5)

Z = 4x₁ + 4x₂

(x₁ , x₂)  = ( 2 , 4)  =>  Z = 24

(x₁ , x₂)  =, ( 6 , 0)   => Z = 24

(x₁ , x₂)  =  ( 0 , 5)  => Z = 20

(x₁ , x₂)  = ( 2 , 4)  => Z = 24   as   x₁ < 6

Hence  

(x₁ , x₂)  = ( 2 , 4)  => Z = 24

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