The company is considering the possibility of allowing backorders to occur for the product. Find the optimal order policy and the optimal total inventory cost given that the annual backorder cost per unit is estimated to be PhP 30. (Q" – S*)? +b= 2Q* G(Q", S*) = K( +h + Ac 2Q*
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- A health and nutrition store stocks a multivitamin with an annual demand of 1,000 bottles has Co probability distribution with μ = 25 and σ = 5. (a) What is the recommended order quantity? (Round your answer to the nearest integer.) = $23.50 and C = $9. The demand exhibits some variability such that the lead-time demand follows a normal (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 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.)In the calculation of an optimal policy for an all-units discount schedule, you firstcompute the EOQ values for each of the three order costs, and you obtain: Q(0) =800, Q(1) =875, and Q(2) =925. The all-units discount schedule has breakpointsat 750 and 900. Based on this information only, can you determine what the optimal order quantity is? Explain your answer.Please 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 0.2
- [item no. 9] In marginal analysis with discrete distributions for single-period inventory models, the value of ML/(ML+MP) is 0.8. The probability distribution of sales is given by the following by the table below. Find the optimal number of units to order. Daily demand 80 90 100 110 120 Probability that demand will be at this level 0.10 0.20 0.30 0.30 0.10 a. 90 units b. 110 units c. 100 units d. 80 units1. Suppose the demand of a product in a retail store is 800 per year and it occurs at a constant rate. Placement of an order of this product to an outside supplier by the store is 40 Dollar. The super market authority has calculated the inventory holding cost per unit per year as 90 cents. Assuming no occurrence of shortages of the product, find a) i. the minimal order quantity of the product from the outside supplier if the product is not allowed to sell during production. ii. the minimal number of orders per year. Explain whether the nearest integer number of orders per year is justified. iii. the cycle time of a lot in months. iv. the annual minimal total cost of ordering and inventory holding for that minimal order quantity. v. the reorder point if the lead time of delivering a lot is 2 days,? b) If the production rate of processing the product is 1200 per year and the set up cost per set up is 65 Dollar. If the selling of the product is allowed during production, determine i) the…A health and nutrition store stocks a multivitamin with an annual demand of 1,000 bottles has Co = $24.50 and Ch = $7.The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with ? = 25 and ? = 5. (a)What is the recommended order quantity? (Round your answer to the nearest integer.) (b)What are the reorder point and safety stock if the store desires at most a 4% probability of stock-out on any given order cycle? (Round your answers to the nearest integer.) reorder pointsafety stock (c)If a manager sets the reorder point at 30, what is the probability of a stock-out on any given order cycle? (Round your answer to four decimal places.) How many times would you expect a stock-out during the year if this reorder point were used? (Round your answer to the nearest integer.)
- Kids’ toys makes an order once each year an the reorder point, without safety stock, is 200 toys. The inventory holding cost is 5$ 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 answerChris usually sells 120 copies of newspaper each day and believe that sale are normally distributed, with a standard deviation of 15 papers. He pays 70 cents for each paper, which sells $1.25. For each unsold paper, he receives 30-cent credit. a) determine how many papers he should order each day b) calculate the stockout risk for that quantity.A 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 .1
- Henrique Correa’s bakery prepares all its cakesbetween 4 a.m. and 6 a.m. so they will be fresh when customers arrive. Day-old cakes are virtually always sold, but at a 50% dis-count off the regular $10 price. The cost of baking a cake is $6, and demand is estimated to be normally distributed, with a mean of 25and a standard deviation of 4. What is the optimal stocking level?A hospital must order the drug Porapill from DaisyDrug Company. It costs $500 to place an order and $30 toreview the hospital’s inventory of the drug. Annual demandfor the drug is N(10,000, 640,000), and it costs $5 to holdone unit in inventory for one year. Orders arrive one monthafter being placed. Assume that all shortages are backlogged.a Estimate R and the number of orders per year thatshould be placed.b Using the answer in part (a), determine the optimal(R, S) inventory policy. Assume that the shortage costper unit of the drug is $100.The reorder point is defined as the lead-time demand for an item. In cases of long lead times, the lead-time demand and thus the reorder point may exceed the economic order quantity Q*. In such cases, the inventory position will not equal the inventory on hand when an order is placed, and the reorder point may be expressed in terms of either the inventory position or the inventory on hand. Consider the economic order quantity model with D = 6,250, C = $40, C₁ = $2, and 250 working days per year. Identify the reorder point in terms of the inventory position and in terms of the inventory on hand for each of the following lead times. (a) 5 days inventory position inventory on hand (b) 15 days inventory position inventory on hand. (c) 25 days inventory position inventory on hand (d) 45 days inventory position inventory on hand