Question: Max31X1............. Edit
Answer: The given problem is,
Subject to the constraint :
Now we follow the chart which are given in the problem.
The solution of the problem in terms of the decision variables :
Here the decision variables are x₁ ,x₂ & x₃.
Therefore the required value of x₁ , x₂ & x₃ are,
x₁ = 13.333 , x₂ = 10.000 , x₃ = 0.000
From the chart we see that the constraint (3) has no upper limit.
Therefore it is not bounded.
So another way we can say that the constraints (1) & (2) are bounded.
If the coefficient of x₁ is increased by 3 then, the value of x₁ will be (13.333+3) = 16.333
Therefore the optimal solution in terms of the decision variables will be :
x₁ = 16.333 , x₂ =10.000 , x₃ = 0.000
And the value of the objective function will be ,
= 506.323+350 = 856.323
If the right hand side of the constraint (1) is increased by 10 then the lower limit will be (77.647+10)=87.647 , and the upper limit will be (107.143+10)=117.143 and the current value will be (90.000+10)=100.000
Then the value of the objective function will be changed into the value of the objective function of the dual problem where the coefficient of x₁ of the objective function will be changed into 100.000
But in this case the value of the objective function of this dual problem is same as the primal problem in which the value of the right hand side of the constraint (1) is increased by 10.
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