Please include as much detail as possible including exact and detailed equations (prefer typed answers so response is legible)

Question #1: A large bakery buys sugar in 100-pound bags. The bakery uses an average of 1,344 bags per year. Ordering cost is $3/order. Annual carrying costs are $14 per per bag. The bakery operates 280 days per year.

1. Determine the economic order quantity,.
2. How many orders per year will there be?
3. Compute the total minimum inventory cost.
4. Determine the number of work-days in an order cycle.
5. If the lead time is 5 days, calculate re-order point (ROP).

Question #2: A toy manufacturer uses 48,000 rubber wheels per year for his popular dump truck series. The firm makes its own wheels which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup costs for a production run of wheels is $45. The firm operates 240 days per year. , Determine a) the optimum run size and b) minimum total annual cost for carrying and setup.

Question #3: A large hospital nursery uses disposable diapers for its newborn babies with an annual demand of 21,900 cases. Ordering costs have been estimated at $50 per order. The hospitals Accounting Department has assigned an annual carrying cost to be 15% of the cost of a diaper case. The purchasing agent for the hospital has an opportunity to take advantage of one of several quantity discounts. The pricing schedule is listed as follows:

Quantity ordered (cases) Unit price

1 4,999 $ 2.45

5000 9,999 2.40

10,000 and over 2.32

1. What is the optimal order quantity?
2. Calculate the annual minimum inventory cost.