Final answer:
The question involves applying KKT conditions to find the global minimum of an optimization problem. However, due to a typo or incomplete information, the objective function and constraints are not clearly defined, making it impossible to solve accurately.
Step-by-step explanation:
The student is tasked with finding the global minimum for an optimization problem using the Karush-Kuhn-Tucker (KKT) conditions. The objective function to be minimized is x(2/1) + x (2/2) - 4x₁ -4x₂ subject to the constraints 2x₁ < 2x₂ and x₁ + x₂ = 3. Given the constraints, we can rewrite the second constraint as an equation by setting x₁ = 3 - x₂ and then the problem becomes one of finding the global minimum of a single-variable function. KKT conditions require us to set up the Lagrangian with the constraints, which include the quadratic terms of the decision variables. However, the provided typo does not clearly demonstrate such a function and is insufficient for demonstrating the full application of the KKT conditions.
For the example given that is a quadratic equation, we would set the equation to zero: 0.000484 -0.00088x = x²x² + 0.00088x -0.000484 = 0 and then use the quadratic formula to find the roots, which gives two possible values for x. However, without a clear and correct representation of the objective function and constraints, the optimization problem cannot be solved accurately using the KKT conditions.