Consider the Following Problem

Question

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The Answer is Since x₁ > 0 and x₃ > 0,it follows that x₁ = 0 and x₃ = 0 cannot be part of the three defining equations at the optimal solution.Since x₂ = 0,then x₁ + x₃

\le

24 and 3 x₁ + 3 x₃

\le

60 or,equivalently,x₁ + x₃

\le

24 and x₁ + x₃

\le

20.This implies that the second constraint (x₁ + x₂ + x₃ ≤ 24)must have some slack,so its constraint boundary equation cannot be a defining equation at the optimal solution.We now have ruled out three of the six constraint boundary equations as being part of the defining equations at the optimal solution.For this three-variable problem,each CPF solution including the optimal solution must have three defining equations.Therefore,the three constraint boundary equations not ruled out must be the defining equations for the optimal solution.These defining equations are x₂ = 0,x₁ + 3 x₂ + 2 x₃ = 30,3 x₁ + 5 x₂ + 3 x₃ = 60.Solving this system of equations yields the optimal solution as (x₁,x₂,x₃)= (10,0,10).

Consider the Following Problem

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