please help

Barney got In = 40 liters of beer that he can either sell or drink. He sets up a dynamic optimization problem to decide what to do. First (in rst period) he decides, which fraction M of the 40 liters he sells at a. price p = 1. Then (second period) he consumes a fraction y; of the rest. His utility from consuming 1: liters is S. For convenience we assume that the beer is a perfectly divisible good. The dynamic optimization problem is henoe specied as follows: T=21 31:3] =32: [0'40]! :1 =22: [011]: (\"(15:31) =ag(a:,y)=a:(1y), f1(1,y)= MI 1:) = 1y. Maw) = 8w: , 11(1) = 0. Th solve the problem we consider for t = 1,2 the Bellman equation Mat) = "Elie! {fr-+1(z.y) + o-n(ar-:+1(Ia 93)} (I E X\")- (a) Determine the value functions no, :21, 02 in the above optimization problem. You may use that the necessary conditions are also suicient. (b) Determine the optimal control (optimal strategy) for .130 = 40. Hon.r much beer do- Barney sell, how much does he drink