The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of itemcost.Quantity1-910 - 9991,000 - 4,9995,000 or morePrice$2.95 per unit$2.50 per unit$2.30 per unit$1.85 per unita. What is the optimal order quantity, given the following price breaks for purchasing the item? [Select]b. What price should the firm pay per unit? $ [Select]c. What is the total annual cost at the optimal behavior? $ [Select]d. What is the holding cost based on the optimal behavior? $ [Select ]

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Answered: a. What is the optimal order quantity,…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section3.8: A Multiperiod Production Model

Problem 22P

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The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost. What is the optimal order quantity, given the following price breaks for purchasing the item? What price should the firm pay per unit? What is the total annual cost at the optimal behavior? Quantity Price 1 – 9 $2.95 per unit 10 – 999 $2.50 per unit 1,000 – 4,999 $2.30 per unit 5,000 or more $1.85 per unit
A mail-order house uses 16,870 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. Number of BoxesPrice per Box1,000 to 1,999$1.25 2,000 to 4,9991.20 5,000 to 9,9991.15 10,000 or more1.10 a.Determine the optimal order quantity. (Round your answer to the nearest whole number.) Optimal order quantity5000 boxes b.Determine the number of orders per year. (Round your answer to 2 decimal places.) Number of order per year
A manager receives a forecast for next year. Demand is projected to be 600 units for the first half of the year and 920 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order. a.Assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods. (Round your answers to the nearest whole number.) Period Order Size 1 – 6 months?_____units 7 – 12 months?_____units b.If the vendor is willing to offer a discount of $10 per order for ordering in multiples of 50 units (e.g., 50, 100, 150), would you advise the manager to take advantage of the offer in either period? If so, what order size would you recommend? (Round intermediate calculations to 2 decimal places.) Period Order Size 1 – 6 months?____ units 7 – 12 months?____…
The demand for a clothing brand is shown in the table below. The cost per order is about $4000. Cost of each unit of clothing = $5. Carrying cost percentage = 25% per item per 5 months. The analysis period = 5 month duration. Month Demand 1 400 2 300 3 200 4 400 5 500 a. Using this data, compute the solutions using the Lot for Lot and Periodic Order Quantity heuristics? Which of these heuristics would perform better and why? b. Assuming that the demand follows a normal distribution with the mean and variance from the data given above, determine the optimal order should be greater or lesser than the single period EOQ model.
Calculate the annual economic order quantity from the information provided below.INFORMATIONGM Electronics expects to sell 800 alarm systems each month of 2022 at R4 000 each. The cost price of each alarm system is R2 000. The inventory holding cost of an alarm system is 1% of the unit cost price. The cost of placing an order for the alarm systems is estimated at R60.
A single inventory item is ordered from an outside supplier. The anticipateddemand for this item over the next 12 months is 6, 12, 4, 8, 15, 25, 20, 5, 10, 20, 5,12. Current inventory of this item is 4, and ending inventory should be 8. Assume aholding cost of $1 per period and a setup cost of $40. Determine the order policyfor this item based onb. Least unit cost
Exercise 2: The demand per year (D) for product X is 12,100 units. The costs of placing an order (S) are $4.50. The unit cost (C) of the item is $25.00. The maintenance cost (H) per unit per year is 30% of the item's cost. 1. Use the economic order quantity (EOQ) model to determine: *Optimal quantity to order* The expected number of orders*Optimal time between orders*The total annual cost of maintaining that optimal amountNOTE: Show calculations of how you arrived at each amount 2. Answer, what are the potential benefits of using EOQ analysis for inventory management? How can you help businesses strike a balance between inventory holding costs and ordering costs?
A book shop is planning to order calendars for sale starting in October. Only one order is placed. The calendars cost $1.50 and the shop sells them for $3 each. At the end of December, the shop reduces the calendar price to $1 and can sell all the surplus calendars at this price. The October-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 proÖt? Why?2. What is the optimal service level?3. How many calendars should the shop order so as to maximize the total expected proÖt?
Quantity discounts. This type of problem can be recognized when a list showing prices for eachquantity range is given along with the basic EOQ information.a. If unit holding cost is constant, use these steps to solve the problem:1. Use Formula 13–2 to find Q.2. Locate Q in the price schedule.3. Compute TC using Formula 13–1 for Q and for all lower-cost price breaks.b. If unit holding cost is a percentage of unit price, use these steps to solve the problem:1. Beginning with the lowest cost, and using the corresponding H for that cost, compute Qusing Formula 13–2. Continue moving up in unit cost until a feasible Q is found.2. Locate the feasible Q in the price schedule.3. Compute TC using Formula 13–9 for Q and for all lower-cost price breaks. Remember to usethe corresponding H for each price.A small manufacturing firm uses roughly 3,400 pounds of chemical dye a year. Currently the firmpurchases 300 pounds per order and pays $3 per pound. The supplier has just announced that ordersof…
A newspaper publisher uses roughly 880 feet of baling wire each day to secure bundles of newspapers while they are being distributed to carriers. The paper is published Monday through Saturday. Lead time is six workdays. What is the appropriate reorder point quantity, given that the company desires a service level of 95 percent, if that stockout risk for various levels of safety stock is as follows: 1,500 feet, .10; 1,900 feet, .05; 2,100 feet, .02; and 2,400 feet, .01?
Ardie Corporation uses 30,000 units. Each order placed is for 1,500 units. The stockout units is 300. Management is willing to accept a stockout probability of 40 percent. The stockout cost per unit is P3.20. What does the total stockout cost? choose the letter of the correct answera. P2,680.00b. P3,680.00c. P4,680.00d. P5,680.00e. P7,680.00
Omega DB Corp. has a policy of maintaining an inventory of finished goods equal to 40 percent of the next month’s budgeted sales. If Omega DB Corp. plans to produce 6,000 units in June, what are budgeted sales for July in units? Budgeted sales for the first six months of 2019 for Omega DB Corp. are listed below: Units:JANUARY 6,000FEBRUARY 7,000MARCH 8,000APRIL 7,000MAY 5,000JUNE 4,000

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a. What is the optimal order quantity, given the following price breaks for purchasing the item? [Select] b. What price should the firm pay per unit? $ [Select] c. What is the total annual cost at the optimal behavior? $ [Select]