Question:

(i) maximizing \(U={{({{x}_{1}}{{x}_{2}})}^{3}}+{{x}_{1}}{{x}_{2}}\), 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 relation between the solutions.