a. Explain verbally all the constraints! b. Define the Hamiltonian function and explain what is the control, state, and co-state variables! c. State completely all first order necessary conditions that will maximize the Hamiltonian function! d. Solve for (), (), and ()!

A consumer wants to maximize his utility from consuming a good (x) in a given state (y) over time (t), specifically for 20 years periods. His problem is defined in the following optimal control model, 20 Max U= Subject to dy dty'=x y(0) = 10 y(20) = 0 A consumer wants to maximize his utility from consuming a good (x) in a given state (y) over time (t), specifically for 20 years periods. His problem is defined in the following optimal control model, 20 Max U= Subject to dy dty'=x y(0) = 10 y(20) = 0