$($iv$)($iv$)$ For $10$ marks $-$ Answer the following three questions.

a$)$ What happens when you initialize the stock at zero inventory? Briefly explain the dynamics experienced.

b$)$ How does the dynamics change as the material delivery frequency increases? Does changing the stock delivery frequency influence stock availability? Explain why or why not with reference to the structure of the model.

c$)$ How does the dynamics change as stock availability fluctuates? Explain.

d$)$ What advice would you give the production supervisor with regards to the situation?