3) A company produces a part that is used in its production process. The company produces the part at a rate of 300 units per day. The daily demand for the product is 180 units. The annual demand for the part is 54,000 units and occurs consistently over the 300 days that the company operates yearly. The company incurs a setup cost of $300 each time the item is produced. The cost of carrying the item in inventory is estimated to be 25 percent of the item's $100 cost. How many units should the company produce each production run to minimize its inventory- associated costs?
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- Consider a hardware supply warehouse that is contractually obligated to deliver 1000units a specialized fastener to a local manufaturing company each week. Each time thewarehouse places an order for these items from its supplier, an ordering and transporationfee off $20 is charged to the warehouse. The warehouse pays $1.00 for each fastener andcharges the local firm $5.00 for each fastener. Annual holding cosst iss 25% off inventoryvalue, or $0.25 per year. The warehouse manager would like to know how much to orderwhen inventory gets to zero.Assume that the warehouse works 50 weeks/year.A retailer uses the order-up-to model to manage inventory of an item in a store. The leadtime for replenishments is four weeks and it can place orders weekly. Weekly demand isPoisson with mean 0.10 unit. Its order-up-to level is five and unfilled demand is backordered. What is the coefficient of variation of its orders?Diskup produces a variety of personal computer products. High-density 3.5-inch disksare produced at a rate of 1,800 per day and are shipped out at a rate of 800 per day. Thedisks are produced in batches. Each disk costs the company 20 cents, and the holdingcosts are based on an 18 percent annual interest rate. Shortages are not permitted. Eachproduction run of a disk type requires recalibration of the equipment. The companyestimates that this step costs $180.a. Find the optimal size of each production run and the time between runs
- Daily demand of a chemical at an oil refinery is normally distributed with a mean of 60 litres and a standard deviation of 7. The supplier reliably delivers the chemical by maintaining a constant lead time of 1 week. There are no delivery charges from the supplier. Sales occur throughout the year. An order placement requires one hour of an administrative employee who is paid $20 per hour. Receiving and storing a chemical shipment requires two workers to work for half an hour. Workers are paid $12 per hour each. Chemical’s purchase price is $500 per litre. Annual cost of capital is 5%. Other holding costs are estimated to be $0.5 per litre. Find the order quantity and the reorder point to satisfy a 95% service level during the lead time. (Round answers to 2 decimal places.)Consider a fixed period inventory model. The daily demand of the product has a mean of 30 and standard deviation of 4; orders are placed every 18 days and shipment lead time is 6 days. The store has a service policy of 96%. What is the inventory required?Motorama TV estimates the annual demand for its TVsis (and will be in the future) normally distributed, with amean of 6,000 and standard deviation of 2,000. Motorama must determine how much production capacity it shouldhave. The cost of building enough production capacity tomake 1,000 sets per year is $1,000,000 (equivalent in presentvalue terms to a cost of $100,000 per year forever). Exclusiveof the cost of building capacity, each set sold contributes$250 to profits. How much production capacity shouldMotorama have?
- Lia ITZY has determined that the annual demand for number 6 screws is 100,000 screws. Lia, who works in her brother’s hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year. QUESTION: How many number 6 screws should Lia order at a time if she wishes to minimize total inventory cost?Lia ITZY has determined that the annual demand for number 6 screws is 100,000 screws. Lia, who works in her brother’s hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year. QUESTION: How many orders per year would be placed? What would the annual ordering cost be?. Goop Inc. needs to order a raw material to make a special polymer. The demand forthe polymer is forecasted to be normally distributed with a mean of 250 gallons anda standard deviation of 100 gallons. Goop sells the polymer for $25 per gallon. Gooppurchases raw material for $10 per gallon and must spend $5 per gallon to dispose of allunused raw material due to government regulations. (One gallon of raw material yieldsone gallon of polymer.) If demand is more than Goop can make, then Goop sells onlywhat it has made and the rest of the demand is lost.a. How many gallons should Goop purchase to maximize its expected profit? b. Suppose Goop purchases 150 gallons of raw material. What is the probability that itwill run out of raw material? c. Suppose Goop purchases 300 gallons of raw material. What are the expected sales (ingallons)? d. Suppose Goop purchases 400 gallons of raw material. How much should it expect tospend on disposal costs (in dollars)? e. Suppose Goop wants to ensure that…
- A company uses the newsvendor model to manage its inventories and faces normallydistributed demand with a coefficient of variation of 0.75. The company decides toorder a quantity that exactly equals the mean of its demand forecast. Which of the following is true regarding this company’s performance measures? a. There is a .50 probability that there is enough inventory to serve all demand.b. Expected inventory equals 50 percent of the mean of the demand forecast.c. The stockout probability is .25.d. Expected inventory is 0.A firm faces a demand of 40,000 units per month for one of its lines of stock. The firm’s cost of holding stock is £2 per unit of average stock per month, and it costs the firm a total of £100 every time it orders and acquires a new shipment of stock. The firm is willing to face stock-outs and the cost of such is £6 per unit of average stock-out per month. Assuming the firm attempts to minimise overall inventory-related costs, how large (approximately) will the firm allow its stock-outs to become before each new stock delivery arrives? A. 782 units B. 577 units C. 904 units D. 981 units * Explain in full detail6. Leaky Pipe, a local retailer of plumbing supplies, faces demand for one of its SKUs at a constant rate of 17,000 units per year. It costs Leaky Pipe $5 to process an order to replenish stock and $2.00 per unit per year to carry the item in stock. Stock is received 12 working days after an order is placed. No backordering is allowed. Assume 365 working days a year. a. Leaky Pipe's optimal order quantity is ______ units. (Enter your response rounded to the nearest whole number.) Part 3 b. The optimal number of orders per year is _____ orders. (Enter your response rounded to the nearest whole number.) Part 4 c. The optimal interval (in working days) between orders is ______ days. (Enter your response rounded to one decimal place.)