Problem 3 Consider the problem Notice that the minimizer is

Problem 3: Consider the problem Notice that the minimizer is x= (0,5). Check whether the optimality conditions are satisfied at that point and provide explanation of the phenomenon?

Solution

f(x1,x2) = 2x1-(5-x2)^3

x1 is positive and x2 is positive

Hence 2x1 >0

Also 2x1<(5-x2)^3

Hence 5-x2 whole cube should be positive

or x2 <5

Thus 0<x1,x2<5 satisfies these.Optimality conditions are satisfied