Use the Excel Solver to solve the following discrete dynamic problem. Repeat the exercise by hand, using the fundamental recursive equation of dynamic programming 11.2-1. max fug X2 t ¼ 0 1 
y2 ðtÞ þ 2u2 ðtÞ 

yðt þ 1Þ ¼ yðtÞ  uðtÞ and y(0) ¼ 5. (Hint: to solve the problem by hand using the standard calculus begin considering the functional J2ðu2Þ ¼ 1  y2 2  2u2 2 which is maximized for u2 ¼ 0 as it turns out to be dJðu2Þ du2 ¼ 4u2. As a second step, consider the functional J1ðu1Þ ¼ 1  y2 1  2u2 1 þ J
2 ¼ 1  y2 1  2u2 1 þ h 1 
y1  u1 2 0 i which is maximized setting dJðu1Þ du1 ¼ 0, then at the end set up J0ðu0Þ ¼ 1  y2 0  2u2 0 þ J
1 . The final solution of the optimal path y*(t) is y(0) ¼ 5, y*(1) ¼ 2.7273, y*(2) ¼ 1.8182, while the OC inputs are u*(0) ¼ 2.2727, u*(1) ¼ 0.9091, and u*(2) ¼ 0.