Please help me with finding the answer for this question, all help is appreciated.

5. (20 points) Solve the following optimal control problem for the exhaustible resource: Maximize f: e'pt In C dt subject to 5: = rx c x(0) =xo x(t) 30 x(T) =xa > 0 where c is the consumption (control variable), x is the amount of resource (state variable), r is rate of return on the resource, and p is the discount rate. Solve for the optimal level of consumption. Also draw the time path of x(t) and c(t) when r > p