multi equation - optimization problem ( known answer, need step by step solution)

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I am new to this forum and I do not have a math background. However, I need to find the solution to the following. The answers are already known, but I do not know how to find these answers, I appreciate your help. (I need to find out how the parameters which are listed at the end such as x1, x2, etc are calculated)

Check the math formula in here