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- Kids’ toys makes an order once each year an the reorder point, without safety stock, is 200 toys. The inventory holding cost is 5$ per toy per year, and cost of stockout is 15$ per toy per year. The following table shows the probability of demand during lead time: Demand during lead time Probability 0 0.05 100 0.15 200 0.35 300 0.25 400 0.2 With a safety stock of 100 toys, the stockout cost is? What is the probability that there is a need to have a safety stock of 100 toys? Explain your answerPlease do not give solution in image format thanku 12. Vintage-looking art replicas are delivered to an art store once a year. The reorder point for the pieces without safety stock is 200 pieces. The carrying cost is $30 per unit per year, and the cost of a stockout is $70 per chair per year. Given the following demand probabilities during the lead time, how much safety stock should be carried? Demand: 0 100 200 300 400 Probability: 0.2 0.2 0.2 0.2 0.2Tobacco is shipped from North Carolina to a cigarette manufacturer in Cambodia once a year. The reorder point, without safety stock, is 200 kilos. The carrying cost is $15 per kilo per year, and the cost of a stockout is $70 per kilo per year. Given the following demand probabilities during the lead time, how much safety stock should be carried? Demand During Lead Time (Kilos) Probability 0 0.1 100 0.1 200 0.2 300 0.4 400 0.2 Part 2 The optimal quantity of safety stock which minimizes expected total cost is enter your response here kilos (enter your response as a whole number).
- Children’s art sets are ordered once each year by AshokKumar, Inc., and the reorder point, without safety stock ( dL ),is 100 art sets. Inventory carrying cost is $10 per set per year, and the cost of a stockout is $50 per set per year. Given the fol-lowing demand probabilities during the lead time, how much safety stock should be carried? DEMAND DURING LEAD TIME PROBABILITY0 .150 .2ROP S 100 .4150 .2200 .11.0A product is ordered once each year, and the reorder point without safety stock (dL) is 100 units. Inventory carrying cost is $10 per unit per year, and the cost of a stockout is $50 per year. Given the following demand probabilities during the reorder period, how much safety stock should be carried? DEMAND DURING REORDER PERIOD PROBABILITY 0 .1 50 .2 ROP 100 .4 150 .2 200 .1The soft goods department for AMG sells 175 units per month of a certain large bath towel. The unit cost of a towel to the manufacturer is R2.50 and the cost of placing an order has been estimated to be R12.00. The organization uses an inventory carrying charge of 27% of the unit cost per year. Determine the optimal order quantity, the order frequency, and the annual holding and setup cost Item Annual Demand Unit Cost A211 800 R9 B390 100 R90 C003 450 R6 D100 400 R100 E707 85 R2000 F660 250 R320 G473 500 R75 H921 100 R75
- Penalty costs can be assessed only against the number of units of demand that cannot be satisfied, or against the number of units weighted by the amount of time thatan order stays on the books. Consider the following history of supply and demandtransactions for a particular part:Number of Items Demand duringMonth Received MonthJanuary 200 520February 175 1,640March 750 670April 950 425May 500 280June 2,050 550Assume that starting inventory at the beginning of January is 480 units.a. Determine the ending inventory each month. Assume that excess demands areback-ordered.b. Assume that each time a unit is demanded that cannot be supplied immediately,a one-time charge of $10 is made. Determine the stock-out cost incurred duringthe six months (1) if excess demand at the end of each month is lost, and (2) ifexcess demand at the end of each month is back-ordered.c. Suppose that each stock-out costs $10 per unit per month that the demandremains unfilled. If demands are filled on a first-come,…A department store uses a (Q, R) policy to control its inventories. Sales of a pocket FM radioaverage 1.4 radios per week. The radio costs the store $50.00, and fixed costs of replenishmentamount to $20.00. Holding costs are based on a 20 percent annual interest charge, and thestore manager estimates a $12.50 cost of lost profit and loss of goodwill if the radio is demanded when out of stock. Reorder lead time is 2 weeks, and statistical studies have shownthat demand over the lead time is accurately described by a Poisson distribution. Find the optimallot sizes and reorder points for this item.A health and nutrition store stocks a multivitamin with an annual demand of 1,000 bottles has Co = $24.50 and Ch = $7.The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with ? = 25 and ? = 5. (a)What is the recommended order quantity? (Round your answer to the nearest integer.) (b)What are the reorder point and safety stock if the store desires at most a 4% probability of stock-out on any given order cycle? (Round your answers to the nearest integer.) reorder pointsafety stock (c)If a manager sets the reorder point at 30, what is the probability of a stock-out on any given order cycle? (Round your answer to four decimal places.) How many times would you expect a stock-out during the year if this reorder point were used? (Round your answer to the nearest integer.)
- A health and nutrition store stocks a multivitamin with an annual demand of 1,000 bottles has Co = $26.50 and Ch = $7. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with ? = 25 and ? = 5. (a) What is the recommended order quantity? (Round your answer to the nearest integer.):________ (b) What are the reorder point and safety stock if the store desires at most a 6% probability of stock-out on any given order cycle? (Round your answers to the nearest integer.) reorder point:________ safety stock:________ (c) If a manager sets the reorder point at 30, what is the probability of a stock-out on any given order cycle? (Round your answer to four decimal places.):________ How many times would you expect a stock-out during the year if this reorder point were used? (Round your answer to the nearest integer.):________An online retailer sells 1,500 t-shirts per year. The cost of the t-shirts to the store is $3.00 and the cost of placing an order is $15 per order. It cost $0.60 per t-shirt per year for the retailer to hold the t-shirts. The retailer sells the t-shirts for $9.99. Determine (a) the optimal order quantity, (b) the order frequency (c) the annual holding and setup cost.Using excel. Apply the EOQ model to the following quantity discountsituation for which D5 500 units per year, Co5 $40, and theannual holding cost rate is 20%. What order quantity do yourecommend?DiscountDiscountCategoryOrder Size(%)unit Cost10 to990$10.002100 or more3$9.70