Spark Industries uses a monthly periodic system to maintain the inventory of batteries it sells.  Below is the sales data for the last 6 months.

a)      What is the company’s average monthly demand for batteries? (2 points)

b)      Assume the standard deviation of demand is 28.1 batteries and Spark Industries wants to be in stock at least 95% of the time.  What is the appropriate restocking level? (2 points)

c)       If there are currently 115 batteries on hand when the order is placed for July, how many batteries should be ordered? (2 points)

Problem 2: Economic Order Quantity (10 points)

A chemical plant orders Chemical X that is used at the rate of 800 barrels per year. Each order that is placed with the supplier costs $45 to process and the annual cost to hold inventory is $80 per barrel.  Delivery lead time of the barrels has averaged 6 days and the plant manager has set a safety stock level of 16 barrels.

a)      What is the economic order quantity? (2 points)

b)      What is the total holding cost for the year? (2 points)

c)       What is the total ordering cost for the year? (2 points)

d)      How many orders will be placed each year? (2 points)

e)      The next order should be placed when inventory drops to what amount? (assume 365 days in one year for converting annual demand to daily demand) (2 points)

Problem 3: Quantity Discounts (5 points)

The UWM Bookstore orders pennants out of a catalog from a supplier.  The demand for these pennants is 12,000 per year.  There is a $25 charge for placing an order and a $10 cost per pennant to hold it in inventory for the year.

a)      What is the economic order quantity? (2 points)

For part b) assume prices for the pennants are based on the quantity purchased, so if less than 100 are ordered, the unit price is $2.50, if 100 to 299 are ordered, the unit price is $2.40, if 300 to 499 are ordered, the unit price is $2.30, and if 500 or more are ordered, the unit price is $2.20.

b)      What order quantity will result in the lowest total annual cost to the UWM Bookstore?  Be sure to show your work for full credit.  (3 points)

Problem 4: Single-Period Inventory System (4 points)

The restaurant you are working at makes one massive batch of potato salad each day.  If you run out before the end of the day, the last few customers are less than satisfied, but if you make too much, it can be sold to the local hog farmer for feed.  Every serving costs $0.23 to make, but can be sold for $1.50 to customers and for $0.07 to the hog farmer.  The average daily demand is for 200 servings with a standard deviation of 20 servings.

a)      What is the target service level? (2 points)

b)      How much potato salad should your restaurant make each day to meet this service level? (2 points)