Investment Optimization Problem : How to determine the suitable amount of money to be borrowed form

Dear Expert
You can see my question in the 1st of the attachment and Its solution will be shown on the 2nd page
For page3-5, It is the guideline for solution implementation
I need you to answer me as follows
1. How to get the solution like 2nd page of the attachment (Step-by-Step like page3-5)
2. How to check this nonlinear problem has a global solution (Step-by-Step)
3.What is the nonlinear type of this problem (convex or concave and which subtype is) by using Hessian Matrix to prove
4.Find the solution of this problem using KKT or Wolfe and Frank
Thank you