Question 1 [10 marks]

A school sees a constant demand rate of 80 boxes of pens per month. The Oxed cost of placing an order is $15, and the holding cost for a box is $2 per year. Answer the following questions.

1. What is the minimum total annual cost that this school can achieve? (5 marks)

2. Suppose later when the school places orders according to the original EOQ, it turns out that the Oxed cost of placing an order is $20. How will the wrong estimation of Oxed cost aect the total annual cost? (5 marks)

Question 2

Derek operates a photo shop which carries instant print Olm. The supplier sets the price of the Olm as in the table below. The shopis average sales are 1000 rolls per year. The annual inventory holding cost is $0.80 per roll and it costs Derek $16 to place an order with the supplier.

Order Quantity	Unit Price
1 to 399	$3.00
400 to 799	$2.88
800 or more	$2.79

Determine

1. Derekis optimal order quantity and minimum total annual cost;

2. The number of orders per year.

Question 3 [12 marks]

A store handles a variety of beauty products. For a particular body wash product, the lead time is two weeks and the weekly demand is normally distributed with a mean of 150 units and a standard deviation of 40 units. The store aims for a service level of 95%.

1. What safety stock should the store hold? (6 marks) 2. At what inventory level should the store place an order? (6 marks)

Question 4

A bookstore sells calendars. The once-a-year order for each yearis calendar arrives in September. The calendars cost $1.50 each and the bookstore sells them for $3 each. If any demand is not met, the bookstore incurs a loss of customer goodwill of $0.5. At the end of December, the bookstore reduces the calendar price to $1 and can sell all the remaining calendars at this price. The September-to- December demand can be approximated by a normal distribution with = 500 calendars and = 120 calendars.

1. What inventory model should be used to determine the order quantity to maximize the total expected profit? Why?

2. What is the optimal service level?

3. How many calendars should the bookstore order so as to maximize the total expected yearly profit?