### 21 the eoq model is solved using calculus but the key intuition is that relevant tot 4300418

21) The EOQ model is solved using calculus but the key intuition is that relevant total costs are minimized when relevant ordering costs equal relevant carrying costs.

22) Safety stock is used as a buffer against unexpected increases in demand, uncertainty about lead time, and unavailability of stock from suppliers.

23) Due to unprecedented growth during the year, Flowers by Kelly decided to use some of its surplus cash to increase the size of several inventory order quantities that had been previously determined using an EOQ model.

**Required:**

Identify whether increasing the size of inventory orders will increase, decrease, or have no effect on each of the following items.

________________a.Average inventory

________________b.Cost of goods sold

________________c.Number of orders per year

________________d.Total annual carrying costs

________________e.Total annual carrying and ordering costs

________________f.Total annual ordering costs

24) The only product of a company has an annual demand of 4,000 units. The cost of placing an order is $20 and the cost of carrying one unit in inventory for one year is $4.

**Required: **

Determine the economic order quantity.

25) Ralph was in the process of completing the quarterly planning for the purchasing department when a major computer malfunction lost most of his data. For direct material XXX he was able to recover the following:

Average inventory level of XXX |
200 |

Orders per year |
40 |

Average daily demand |
48 |

Working days per year |
250 |

Annual ordering costs |
$4,000 |

Annual carrying costs |
$6,000 |

Ralph purchases at the EOQ quantity level.

**Required: **

Determine the annual demand, the cost of placing an order, the annual carrying cost of one unit, and the economic order quantity.

26) Clothes, Inc., has an average annual demand for red, medium polo shirts of 25,000 units. The cost of placing an order is $80 and the cost of carrying one unit in inventory for one year is $25.

**Required: **

a.Use the economic-order-quantity model to determine the optimal order size.

b.Determine the reorder point assuming a lead time of 10 days and a work year of 250 days.

c.Determine the safety stock required to prevent stockouts assuming the maximum lead time is 20 days and the maximum daily demand is 125 units.

27) An inventory item of XYZ Manufacturing has an average daily demand of 10 units with a maximum daily demand of 12 units. The economic order quantity is 200 units. Without safety stocks, the reorder point is 50 units. Safety stocks are set at 94 units.

**Required: **

a.Determine the reorder point with safety stocks.

b.Determine the maximum inventory level.

c.Determine the average lead time.

d.Determine the maximum lead time.

28) For supply item ABC, Andrews Company has been ordering 125 units based on the recommendation of the salesperson who calls on the company monthly. A new purchasing agent has been hired by the company who wants to start using the economic-order-quantity method and its supporting decision elements. She has gathered the following information:

Annual demand in units |
250 |

Days used per year |
250 |

Lead time, in days |
10 |

Ordering costs |
$100 |

Annual unit carrying costs |
$20 |

**Required: **

Determine the EOQ, average inventory, orders per year, average daily demand, reorder point, annual ordering costs, and annual carrying costs.