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 ½UðCðtÞÞdt ¼ Z 1 0 ½UðfðKðtÞÞ  K0 ðtÞÞdt s:t: Kð0Þ ¼ 5 and KðTÞ ¼ 3 where the production function is: fðKðtÞÞ ¼ rKðtÞ ðr > 0Þ with r ¼ 5% and the utility function is in the following form: UðCðtÞÞ ¼ Ub  1 b Cb ðb > 0Þ with Ub ¼ 10, b ¼ 0.5. Also, find the optimal numerical consumption path CðtÞ ¼ rKðtÞ  K'