Problem I $(10$ points$)$

A milk cooperative collects fresh milk from farmers in the region and uses it to produce pasteurized milk and its derivatives. The cooperative's products are then distributed regionally, which allows the cooperative to generate interesting revenues. Considering the perishable nature of milk, the

cost of launching an order is $$300$ and the annual cost of holding $1$ liter of milk in inventory is $$2.$

The annual demand for the product is $15,000$ liters and the delivery lead time is $5$ days. The

company works $5$ days a week for $52$ weeks a year.

$($a$)$ Determine the economic order quantity and compute the total inventory management costs

for the year. $(2$P$)$

$($b$)$ Determine the reorder point. $(2$P$)$

$($c$)$ How many orders will be launched per year? $(2$P$)$

$($d$)$ Assuming a decrease in the ordering costs, would the company order less quantity more

frequently, or more quantity less frequently? Explain. $(2$P$)$

$($e$)$ Assuming demand is variable and normally distributed with a standard deviation of $5$ liters per

day. What would the new reorder point if you want to keep a service level of $95\%?(2$P$)$