A retailer determines that the cost of ordering and storing units of a product can be modelled by C(x)= 3x + 2000 / x, 0 < x < 200. Find the order size that will minimise ordering and storage cost
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A retailer determines that the cost of ordering and storing units of a product can be modelled by C(x)= 3x + 2000 / x, 0 < x < 200. Find the order size that will minimise ordering and storage cost.
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- Rocky Mountain Tire Center sells 20,000 go-cart tires per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year.The purchase price is $20 per tire if fewer than 500 tires are ordered, $18 per tire if 500 or more-but fewer than 1,000- tires a re ordered, and $17 per tire if I ,000 or more tires areordered.a) How many tires should Rocky Mountain order each time it places an order?b) What is the total cost of this policy?The best quantity to order One of the formulas for inventorymanagement says that the average weekly cost of ordering, payingfor, and holding merchandise iswhere q is the quantity you order when things run low (shoes,TVs, brooms, or whatever the item might be); k is the cost ofplacing an order (the same, no matter how often you order); c isthe cost of one item (a constant); m is the number of items soldeach week (a constant); and h is the weekly holding cost per item(a constant that takes into account things such as space, utilities,insurance, and security). Find dA>dq and d2A>dq2.____ is the ordering model which calculates the timing of the inventory order:Select one:a. ABC modelb. Fixed order quantity modelc. EOQ model d. Reorder point model
- Rocky Mountain Tire Centre sells 20,000 tires of a particular type per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20. per tire if fewer than 500 tires are ordered, $18. Per tire if more than 500 but fewer than 1,000 tires are ordered and $17. per tire if 1,000 or more tires are ordered. Quantity Unit Price 1-499 $20. 500-999 $18. 1000 & over $17 Based on available information, lead time demand for CD-ROM drives averages 50 units (normally distributed), with a standard deviation of 5 drives. Management wants a 97% service level. What value of Z should be applied? How many drives should be carried as safety stock?Suppose the monthly demand for automobile tires at a tire dealer is Normally distributed with a mean of 250 tires and a standard deviation of 50 tires. How many tires must the store have in inventory at the beginning of each month to meet the demand 95% of the time?Rocky Mountain Tire Centre sells 20,000 tires of a particular type per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20. per tire if fewer than 500 tires are ordered, $18. Per tire if more than 500 but fewer than 1,000 tires are ordered and $17. per tire if 1,000 or more tires are ordered. How many tires should Rocky Mountain order each time it places an order? Quantity Unit Price 1-499 $20. 500-999 $18. 1000 & over $17 Based on available information, lead time demand for CD-ROM drives averages 50 units (normally distributed), with a standard deviation of 5 drives. Management wants a 97% service level. What value of Z should be applied? How many drives should be carried as safety stock?
- Vetox sells industrial chemicals. One of their inputs can be purchased in either jugs orbarrels. A jug contains one gallon, while a barrel contains 55 gallons. The price pergallon is the same with either container. Vetox is charged a fixed amount per orderwhether it purchases jugs or barrels. The inventory holding cost per gallon per monthis the same with either jugs or barrels. Vetox chooses an order quantity to minimizeordering and holding costs per year. Would Vetox purchase a greater number of gallonswith each order if it purchased with jugs or with barrels?a. They would order a greater number of gallons with barrels.b. They would order the same number of gallons with either container.c. They would order a greater number of gallons with jugs.d. They might order a greater number of gallons with jugs or with barrels, depending onvarious factors like the demand rate, ordering cost, and holding cost.World’s Greatest Coffee EOQ Problem A natural food store carries a brand of coffee called World’s Greatest Coffee. The following data shouldbe used in your calculations.Demand/Sales = 10 cases of coffee per week (you will need to convert this to an annual amount)Ordering Cost = $12 per orderCarrying Charge = 18% per yearUnit Cost = $75 per case Answer the following questions and be sure to show your computations. You can use whatever symbolyou need for square root, if typing in Word.1. How many cases should be ordered at a time? (This number will be the EOQ)2. How often should the coffee be ordered?3. What is the annual cost or ordering the coffee? What is the annual cost of carrying the coffee?And what is the total cost (ordering and carrying costs added together)?4. Name three reasons or factors that might cause the firm to order a larger or smaller amountthan the EOQ. Scoring – 20 possible pointsSection Possible PointsQuestion 1 – EOQ computation 4Question 2 – Frequency of…With a probabilistic model, increasing the service level A. will decrease the level of safety stock level. B. will increase the cost of the inventory holding. C. will have no impact on the cost of the inventory policy. D. will reduce the cost of the inventory holding.
- Vallie Enterprise sells a product that cost $200 per unit and has a monthly demand of 500 units. The annual holding cost per unit is calculated as 2% of the unit purchase price. It costs the business $30 to place a single order. The maximum number of units sold for any one week is 150 and minimum sales 80 units. The vendor takes anywhere from 2 to 4 weeks to deliver the merchandise after the order is placed. The EOQ model is appropriate. i) What is the cost minimizing solution for this product each year? ii) Determine the re-order level, minimum inventory level and maximum inventory level for the product.A firm uses the order-up-to model to manage its inventory. It wants to increase its in-stockprobability while decreasing its holding costs (i.e., reducing its average inventory). Which ofthe following actions will help to achieve this goal? (Consider each action independently.)I. Decrease the lead time.II. Increase the order-up-to level.III. Increase the average quantity on order.a. Only Ib. Only IIc. Only IIId. I and IIe. I and IIIf. II and IIIg. Any of them will help (that is I, II, or III).h. None of them will help.A company has an annual demand of 2500 units. The cost to place an order to replenish inventory is SR18.75 per order, and annual inventory holding cost per unit is SR1.5. On average, delivery of an order takes 3 working days (Lead time). Assume the store is open 250 days per year. What is the optimal order size? What is the optimal number of orders per year? What is the optimal number of days between orders? What is the Reorder Point (ROP)? What is the Reorder Point (ROP) with 2 days safety stock.