3. The manager at Goodstone Tires, a distributor of tires in Illi- nois, uses a continuous review policy to manage inventory. The manager currently orders 10,000 tires when the inven- tory of tires drops to 6,000. Weekly demand for tires is nor- mally distributed, with a mean of 2,000 and a standard deviation of 500. The replenishment lead time for tires is two weeks. Each tire costs Goodstone $40, and the company sells each tire for $80. Goodstone incurs a holding cost of 25 per- cent. How much safety inventory does Goodstone currently carry? At what cost of understocking is the manager's current inventory policy justified? How much safety inventory should Goodstone carry if the cost of understocking is $80 per tire in lost current and future margin?
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- The buyer for Needless Markup, a famous “high end” department store, mustdecide on the quantity of a high-priced woman’s handbag to procure in Italy for thefollowing Christmas season. The unit cost of the handbag to the store is $28.50 andthe handbag will sell for $150.00. Any handbags not sold by the end of the seasonare purchased by a discount firm for $20.00. In addition, the store accountantsestimate that there is a cost of $0.40 for each dollar tied up in inventory, as thisdollar invested elsewhere could have yielded a gross profit. Assume that this costis attached to unsold bags only.a. Suppose that the sales of the bags are equally likely to be anywhere from 50to 250 handbags during the season. Based on this, how many bags should thebuyer purchase? (Hint: This means that the correct distribution of demand isuniform. You may solve this problem assuming either a discrete or a continuousuniform distribution.)b. A detailed analysis of past data shows that the number of bags sold is…3. Cynthia Knott’s oyster bar buys fresh Louisiana oysters for $5 per pound and sells them for $12 per pound. Any oysters not sold that day are sold to her cousin, who has a nearby grocery store, for $1 per pound. Cynthia believes that demand follows the normal distribution, with a mean of 100 pounds and a standard deviation of 15 pounds. a) What is the cost of underestimating demand for each pound? b) What is the overage cost per pound? c) How many pounds of oyster should she order each day? d) What is the stockout risk for this order size?Green Thumb, a manufacturer of lawn care equipment, has introduced a new product. Each unit costs $180 to manufacture, and the introductory price is $250. At this price, the anticipated demand is normally distributed, with a mean of μ = 300 and a standard deviation of σ = 60. Any unsold units at the end of the season are unlikely to be valuable and will be disposed of in a post-season sale for $50 each. How many units should Green Thumb manufacture for sale? What is the expected profit from this policy? On average, how many customers does Green Thumb expect to turn away because of stocking out? Please show workings and formula in excel
- Forrest and Dan make boxes of chocolates for which the demand is uncertain. Forrest says, “That’s life.” On the other hand, Dan believes that some demand patterns exist that could be useful for planning the purchase of sugar, chocolate, and shrimp. Forrest insists on placing a surprise chocolatecovered shrimp in some boxes so that “You never know what you’ll get.” Quarterly demand (in boxes of chocolates) for the last 3 years follows: Quarter Year 1 Year 2 Year 3 1 2 3 4 3,000 1,700 900 4,400 3,300 2,100 1,500 5,100 3,502 2,448 1,768 5,882 Total 10,000 12,000 13,600 a. Use intuition and judgment to estimate quarterly demand for the fourth year.b. If the expected sales for chocolates are 14,800 cases for year 4, use the multiplicative seasonal method to prepare a forecast for each quarter of the year. Are any of the quarterly forecasts different from what you thought you would get in part (a)?Green Thumb, a manufacturer of lawn care equipment has introduced a new product. Each unit cost $150 to manufacture, and the introductory price is to be $200. At this price, the anticipated demand is normally distributed, with a mean of 100 and a standard deviation of 40. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a fire sale for $50 each. It costs $20 to hold a unit in inventory for the entire season. How many units should Green Thumb manufacture for sale? What is the cycle service level (probability of not stocking out) associated with this policy? If the holding costs increase, how does this affect the optimal number of units to manufacturer and the cycle service level? *Note you can construct a graph if you preferA supermarket in Seattle must decide how many wedding cakes to prepare for the upcomingweekend. Cakes cost $33 each to make, and they sell for $60 each. At the very last hour of theday, any unsold boxes are reduced to “half-price”. Holding cost is negligible. Analysis of recentdemand resulted in the following table: Demand Probability 0 .15 1 .35 2 .30 3 .20 How many cakes should be prepared to maximize expected profit?
- The Rahway, New Jersey, plant of Metalcase, a manufacturer of office furniture, produces metaldesks at a rate of 200 per month. Each desk requires 40 Phillips head metal screws purchasedfrom a supplier in North Carolina. The screws cost 3 cents each. Fixed delivery charges and costsof receiving and storing shipments of the screws amount to about $100 per shipment, independently of the size of the shipment. The firm uses a 25 percent interest rate to determineholding costs. Metalcase would like to establish a standing order with the supplier and is considering several alternatives. What standing order size should they use?Letherin Hides is a company that makes boots specifically targeting college students. Forecasts of sales for the next year are 200 in the summer, 450 in the fall, and 500 in the winter. Accessories that are used on the boots are purchased from a supplier for $31.66. The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06(31.66)=$1.9 per quarter (rounded figure). Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6.00 per hour. In the fall, labor is more difficult to keep, and the owner must pay $6.50 per hour to retain qualified help. Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour. Each boot design takes 2 hours to complete. How should production be planned over the three quarters to minimize the combined production and inventory holding costs? The table below provides…Please do not give solution in image format thanku Deltic sells this component for 55 per unit with a 4-month delivery lead time. Assume Deltic covers all transportation and related processing until delivery. TCX’s demand forecast for the upcoming selling season (12 months) is a normal distribution with mean 13500 and standard deviation 3736,4 . TCX sells each unit, after integrating their proprietary software, for 135. Assume that TCX uses a holding cost rate of 25 %, and any leftover units can be sold for 30 on average. Due to the long lead time and high minimum order quantity required, TCX is planning on a single order from Deltic to meet their needs in the next year. How many of these components should TCX order? Calculate the resulting expected annual profits for TCX.
- 1. The demand for a product of Carolina Industries varies greatly from month to month. Based on the past three years of data, the following shows the monthly demand at Carolina Industries. Unit Demand # Months 300 6 400 8 500 12 600 10 A.If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product? B. What are the variance and the standard deviation for the number of units demanded?The bookstore at Tech purchases jackets emblazoned withthe school name and logo from a vendor. The vendor sellsthe jackets to the store for $38 apiece. The cost to the bookstore for placing an order is $120, and the annual car-rying cost is 25% of the cost of a jacket. The bookstore manager estimates that 1700 jackets will be sold during theyear. The vendor has offered the bookstore the followingvolume discount schedule: Order Size Discount1–299 0%300–499 2%500–799 4%800 5% What is the bookstore’s optimal order quantity, given thisquantity discount information?XYZ is a multinational corporation based in the US. Its manufacturing facilities arelocated in Pittsburgh and hence its labor and manufacturing costs are incurred in USdollars (USD). A large fraction of its sales, however, are made to German customers whopay for the goods in Deutschemarks (GDM). There is a six-month lead time between theplacement of a customer order and delivery of the product. XYZ's cost of production is80% of the sale price. Suppose XYZ receives a $1MM GDM order and that the currentUSD/GDM exchange rate is 0.60 (i.e. 1 GDM = 0.60 USD). The cost of production of thisorder is $480,000 (0.60 x $1MM x 0.80). The exchange rate six months from now is, ofcourse, uncertain in which case XYZ is exposed to exchange rate risk.RequiredExplain how the company can use forward contract for hedging purposes