Optimal consumption Ramsey model. Solve the Ramsey problem, finding the optimal capital path K*(t), such that the following functional is maximized: UðKÞ ¼ Z 1 0 ½UðCðtÞÞe t=4 dt ¼ Z 1 0  ln 2K  K' e t=4 dt s:t: Kð0Þ ¼ 5 and KðTÞ ¼ 7