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**For all the problems, to receive full scores, you have to show your complete and accurate work. If you only provide the final answers without showing your computations, you will not be assigned a full score (or you will miss the opportunity of receiving partial credit).**

**Problem 1: Economic Order Quantity (10 points)**

A chemical plant orders barrels of argon that is used at the rate of 800 barrels per year. Each order that is placed with the supplier costs $20 to process and the annual cost to hold inventory is $125 per barrel. Delivery lead time of the barrels has averaged 13 days, but since this lead time can vary the plant manager has set a safety stock level of 82 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? You can leave this answer as a decimal. (2 points)
- e)The next order should be placed when argon inventory drops to what amount? (assume 365 days in one year for converting annual demand to daily demand. You can leave this as a decimal.) (2 points)

**Problem 2: Quantity Discounts (5 points)**

The UWM Bookstore orders bumper stickers out of a catalog from a supplier. The demand for these bumper stickers is 7,396 per year. There is an $80 charge for placing an order and a $10 cost per bumper sticker to hold it in inventory for the year.

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

For part b) assume prices for the bumper stickers are based on the quantity purchased, so if less than 100 are ordered, the unit price is $1.12, if 100 to 299 are ordered, the unit price is $1.10, if 300 to 499 are ordered, the unit price is $1.08, and if 500 or more are ordered, the unit price is $0.99.

**Problem 3: Periodic Review System (6 points)**

You work for a retailer that uses a monthly periodic system to maintain the inventory of microwaves it sells. Below is the sales data for the last 6 months.

Month |
May’16 |
June’16 |
July’16 |
Aug’16 |
Sept’16 |
Oct’16 |

Units Sold |
107 | 175 | 146 | 129 | 156 | 158 |

- a)What is the company’s average monthly demand for microwaves? (2 points)
- b)Assume the standard deviation of demand is 24.0 microwaves and the company wants to be in stock at least 95% of the time. What is the appropriate restocking level? (2 points)
- c)If there are currently 89 microwaves on hand when an order is placed, how many microwaves should be ordered? (2 points)

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

The restaurant you are working at makes one massive batch of macaroni and cheese 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 and can be sold for $2.25 to customers. You have to pay $0.02 per serving to transport the extra servings to the hog farmer, but the hog farmer will pay you $0.09 per serving. The average daily demand is 121 servings with a standard deviation of 17 servings.

- a)What is the target service level? (2 points)
- b)How many servings of macaroni and cheese should your restaurant make each day to meet this service level? (2 points)

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