MATLAB short implementation of a dynamic optimization approach

For a project I need to implement the following task:

In this task you should solve a lot size scheduling problem via dynamic optimization.
For this task is no theoretical knowledge about lot sizing problems or dynamic optimization requird.

Task c:

Write the recursive function "valuefunction" with the input arguments S and t (step/time period) and the output argument V (value).
- Define the demand vector = [3,4,3,4,3]
- Define the decision vector x = [0:10]
-- Calculate
V(S,t) = max x (utility(S,x,W) + V(Snew, t+1)) with the termination condition V(S,6) for alle S.

Note: the maximum has to be considered for all decisions. Use the transformationfunction (will be provided by me) with the demand of the corresponding step.

Task 2: Calculate and plot V(S,1) for S in the set 0:1:10

Task 3: Count how often "valuefunction" will be called upon by calculating V(0,1). You are permitted to adjust the corresponding functions.