Respuesta :
The objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, satisfies the KKT condition.
To find the optimal solution graphically, first plot the points (-1,0), (0,1), (1,0), and (0,-1) on the coordinate plane. These points form a square. The objective function for this problem is to minimize -x1 + x2. So we need to find the point on the square that is as low as possible on the y-axis (because the y-axis represents x2).
The constraint in question is x1 + x3 - 2x1 = 0, which can be rewritten as x3 = 2x1. Since x1 and x3 are variables, this represents a line on the coordinate plane. You can draw this line by selecting two points on this line and connecting them with a line. For example, you can select points (-1, -2) and (1, 2). These points lie on the line x3 = 2x1 and the connecting lines are plotted in the coordinate plane.
We can find the best solution by finding the point on the square that is the lowest possible on the straight line of y-axis and x3 = 2x1. The point that satisfies both of these conditions is the point (0,-1). This is the best solution for your problem.
To answer the second part of the question we need to determine whether the Fritz-John condition or the KKT condition is the optimal solution. The Fritz-John condition is an optimality requirement involving an objective function and problem constraints. A KKT condition is a necessary and sufficient condition for optimality that includes an objective function, a constraint, and a multiplier associated with the constraint.
The Fritz-John condition is not considered optimal for this problem. This is because the optimal solution does not satisfy the condition x1 + x3 – 2x1 = 0. The point (0,-1) does not satisfy the condition because it is not on the line x3 = 2x1.
KKT conditions are considered to be the best solution. This is because the point (0,-1) is a legal point (it lies on the square representing the legal region) and the global minimum of the objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, which satisfies the KKT condition.
Read more about KTT condition on brainly.com/question/13258612
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