A wealthy couple have three children named Xena, Yuri, and Zoe. To give their children a lesson in entrepreneurship, the parents have decided to invest a total of $35,000. They asked their children what they could accomplish if they were given some of the money. Xena said, "Whatever you give me, I will return not only the principal but the square root of the principal as well." (For example, if she were given $1600, she would return 1600+p1600 = 1640 dollars.) Yuri thought that he could do better than his younger sister: "I'll return the principal plus twice the square root of the principal", he boasted. Their older sister Zoe felt that she had to do even better: "I'll return the principal plus three times the square root of the principal." The parents wonder how the $35,000 should be distributed to their children, so as to maximize the total net return.

 

(a) Formulate a model for this problem.

(b) Obtain the solution using the Solver.