A fast-food restaurant buys hamburger buns from a national bakery supplier. The daily usage of buns at the restaurant is normally distributed with an average of 160 and standard deviation of 10. It takes 4 days for the supplier to deliver. The purchasing agent at the restaurant has established a 99.7% service level. Construct a model to determine:
a) The Safety Stock and Reorder Point for the restaurant.
b) The fast-food restaurant now considers ordering hamburger buns from a local bakery. To estimate its costs, the restaurant assumes now those buns are used at the (constant) rate of 100 per day and are purchased at $0.025 per bun. And it costs $1 for each order placed and the annual inventory holding cost per unit is 25% of the unit purchase cost. How much should be ordered (rounded to the nearest integer) each time to minimize the restaurant's total annual costs? And what is the length of order cycles (i.e. time between orders) in days? Assume the restaurant operates 360 days per year.