Question $2$

The Countryside Restaurant serves premium beef steaks to its customers. The daily demand for the beef is normally distributed, with an average $77$ kilograms and a standard deviation $10\mathrm{.}5$ kilograms. The lead time to receive an order of beef from the local supplier is normally distributed with a mean of $1\mathrm{.}5$ days and a standard deviation of $0\mathrm{.}5$ day. The beef costs $3\mathrm{.}8$ OMR per kilogram. Reorder cost is $14$OMR, and holding cost is $45\%.$

a$)$ Determine the re$-$order point if the restaurant wants to maintain a $95\%$ service level. $(2$ mark$)$

b$)$ What is the annual cost of the safety stock?

$($I mark$)$

c$)$ What change will happen to the restaurant's safety stock of beef, if the restaurant manager decides to switch to another supplier who can deliver with constant lead time of $3$ days?

$(2$ marks$)$