Question: Solve the problems of:

(i) Maximizing \(U={{\left( {{x}_{1}}{{x}_{2}} \right)}^{3}}+{{x}_{1}}{{x}_{2}}\), subject to \({{p}_{1}}{{x}_{1}}+{{p}_{2}}{{x}_{2}}=y\), and

(ii) Maximizing \(U=\ln {{x}_{1}}+\ln {{x}_{2}}\), subject to \({{p}_{1}}{{x}_{1}}+{{p}_{2}}{{x}_{2}}=y\); and explain the relationship between the solutions.