Question 1a. Give two examples each of a functional product and an innovative product.b. Characterize functional/innovative products by choosing the appropriate adjective from the last column.Product CharacteristicLifecycle lengthFunctional ProductInnovative ProductChoose FromLong/ShortContribution marginHigh/LowProduct varietyLot/LittleForecast errorsLarge/SmallStockout ratesHigh/LowForced end-of-season markdownsFrequent/RareOrder lead timeLong/Shortc. It is claimed that a supply chain has two functions: a physical function, and a market mediation function.Explain what these terms mean.d. Supply chains are generally of two types: physically efficient supply chains, and market responsive supply chains. What type of supply chain would be suitable for a functional product? Why?Question 2a. How do demand variability and lead time impact a firms inventory levels?Consider a firm redesigning its logistics network. What are the advantages to having a small number ofcentrally located (large) warehouses as opposed to a large number of decentralized (small) warehouses closer tothe end customers?b. Combining two warehouses into one is most beneficial when the demands at the two warehouses arenegatively correlated. True or False? Explain your reasoning.c. A firm operates both a large national DC and numerous smaller regional warehouses. Which types ofproducts should be stored centrally and which ones regionally?d.Question 3The boardwalk on the Paradise City beach is 4 miles long with mile markers at 0, 1, 2, 3, and 4 miles, Thereare 100 customers at each mile marker and each customers demand for ice cream is given by the function: D =24 4d, where d = distance between customer and nearest ice cream vendor.01A234BThere are two ice cream vendors (A and B) and they are currently located at mile markers 1 and 2 as shown above. a. Find out the demand at each vendor and total demand for the system.b. Are these the best locations of the vendors from the systems point of view? If not, suggest better locations for the vendors. What is the total system demand now?c. Compute how much and to whom an incentive should be offered so that the vendors relocate to the optimal locations from the systems point of view? (Assume one unit of ice cream generates $1.50 in profit.)Question 4RFC Bearings has just entered the U.S .market. It has three major DCs in the Atlanta, Boston, and Chicago areas.Annual demand served by each DC is estimated to be:Atlanta 10,000Boston 20,000Chicago 15,000Four plants (Memphis, Philadelphia, Toledo) supply the DCs. Per-unit transportation costs and plant capacities aregiven in the following table:PlantLocationDistributionCenterAtlantaMemphis$3Philadelphia5Toledo6PlantCapacityBostonChicago97246230,00035,00035,000Using the notation:XMA = Qty shipped from Memphis to AtlantaXMB = Qty shipped from Memphis to Boston, etc.,write down a model that will determine the optimal demand allocation (i.e. minimize transportation costs.)Suppose now that the three locations (Memphis, Philadelphia, Toledo) are potential locations, i.e., each plantwould only be constructed if it improves overall cost (i.e., transportation plus plant fixed costs). The data isrepeated here with the (annualized) plant fixed costs shown additionally.PlantLocationDistributionCenterAtlantaMemphis$3Philadelphia5Toledo6PlantCapacityBostonChicago972462AnnualizedFixed Costs30,00035,00035,000$50,00045,00048,000What changes would you make to the model in part (a) so that we can determine the optimal locations of the plants as well as the optimal demand allocation (i.e. minimize both transportation as well as fixed costs). [Do not attempt to solve this modelyou are only asked to write down the model, i.e. objective function and constraints.]Question 5Consider the following data pertaining to a distribution center.ParameterMean Weekly DemandStandard Deviation of Weekly DemandLead Time# of weeks in yearOrdering cost:Holding cost:Cycle service level:MeasureValue100302 Weeks50$50 /order$4 /unit /week (This is H, not hc eq. (11.2) on p. 273 of text.)97%Computationorder quantitycycle inventorysafety inventoryreorder levelannual inventory holding costnumber of orders per yearannual ordering costQuestion 6Suppose the 100 retail stores of a supermarket chain have identical weekly demand for a product (mean 200, standard deviation 120). There is zero correlation between the retailers demands. The lead time to replenish each retail store is 4 weeks. A cycle service level of 95% is desired.a. If each retail store maintains its own dedicated warehouse, how much safety stock is needed at each store?b. What is the total safety stock across all stores?It is now proposed to have a central DC servicing all 100 retailers. The lead time to replenish the DC is thesame (4 weeks). How much safety stock is needed at the DC to maintain the same cycle service level?c. If annual inventory holding cost is $50/unit/year, how much money was saved as a result of the decrease in the safety stock?dQuestion 7AspenWear, a retailer of ski wear needs to place an order for the Mirabelle, a designer ski jacket for the high-end market. The jacket retails for $600 and costs AspenWear $250 from a source in China. Due to fickle customer tastes, any surplus jackets at the end of the ski season cannot be carried over to the next season but must be disposed of. A bargain discounter has offered to buy these jackets at $150 each (and plans to mark them up to $300). Also, because of the long lead times involved in sourcing from China, there is realistically only one opportunity to place an order during each season (in November of each year so that the jackets will be ready by the following August). From past history, AspenWear believes that demand for the Mirabelle can be represented by a normal distribution with mean 6000 and standard deviation 3600. Their current ordering rule is as follows: Order Quantity = Mean Demand + (1/3)*(Standard Deviation) a. Compute the order quantity that will maximize AspenWears expected profit.b. Compare the two quantities (the one computed above plus the current rule) in terms of the followingperformance measures: expected sales, expected profit, expected overstock, and fill rate. (It would be helpful if you display your results in a 2 x 4 table2 quantities, 4 performance measures.)Question 8A movie studio sells the latest movie on DVD to Blockbuster at $10 per DVD. The marginal production costfor the movie studio is $2 per DVD. Blockbuster prices each DVD at $25 to its customers. DVD s are kept onthe regular rack for a one-month period, after which they are discounted down to $3. Blockbuster places asingle order for DVDs. Their current forecast is that sales will be normally distributed, with a mean of 50,000and a standard deviation of 30,000.a. How many DVDs should Blockbuster order? What is its expected profit?b. What is the profit that the studio makes given Blockbusters actions?c. The studio is offering Blockbuster a deal: They will sell the DVD to blockbuster at $5 each in return for a65-35 split of the revenue (65% to Blockbuster). Should Blockbuster agree to this deal?