Do you agree with the following statement: $$According to the EOQ model, when the setup cost

increases, the optimal order cycle has to increase.$$ Explain. $($Hint: The optimal batches per

year are given by D$/$EOQ and so the $$optimal order cycle,$$ defined as the time from the two

adjacent orderings, is equal to EOQ$/$D$.)$

$($b$)$ Suppose you operate a store. The weekly average demand for an item sold in your store is $20$

units. Your upstream supplier charges $$100$ for each item sold to you. The annual holding

cost is $20\%$ of the item cost. It costs $$160$ to place an order. The lead time is $1$ week and your

store operates $50$ weeks per year.

i$)$ What is the optimal order quantity?