Final answer:
To find the optimal solution for the given concave NLP problem using the K-T conditions, set up the necessary equations and solve them simultaneously.
Step-by-step explanation:
The student has asked to find the optimal solution to a concave Nonlinear Programming (NLP) problem using the Karush-Kuhn-Tucker (K-T) conditions. While the problem statement has not specified any constraints, the usage of K-T multipliers typically implies that there are constraints which the student might have left out of the question.
Normally, one would need to specify the constraints to formally use the K-T conditions. Assuming there are constraints, we would set up the Lagrangian function with the objective function's terms and the constraints multiplied by their respective K-T multipliers, λ1 and λ2. The partial derivatives of the Lagrangian with respect to x1, x2, x3, λ1, and λ2 would be taken and set to zero to solve the K-T conditions. This process identifies the points that could potentially maximize the objective function.
Without the explicit constraints, we cannot provide a numerical solution, but the described method is how one would approach such problems using K-T conditions. To illustrate, for a utility maximization problem with a budget constraint, one might use an equation involving prices and quantities purchased (Π×QΠ¹ + Π₂×Q₂) to define the latter.