1. Gator Depot Company (GDC) is a large chain of home improvement stores which owns several hundred retail stores in the Eastern United States. Hot&Cold Company (H&C) is the sole HVAC equipment supplier for GDC. The most popular HVAC unit that GDC sells is H&CPXX, where XX indicates the model year of the unit. For example H&CP23 would be the 2023 model of H&CP. H&C Company always introduces its new model in the December of each year and these models are available for sale in the GDC stores on January 1 of the following year. To be able to plan its production and place the necessary parts and components orders with its suppliers, H&C requires GDC to place its order for the entire year in the first week of December of the previous year. Although GDC places its order for the entire year, for inventory and working capital planning purposes, they need quarterly forecasts. GDC’s sales and marketing department provided the following quarterly sales data for H&CP, expressed in thousands of units.Year Quarter Sales( in 1000 units)2019 1 50 2 28 3 82 4 702020 1 54 2 26 3 88 4 722021 1 58 2 30 3 91 4 712022 1 60 2 31 3 94 4 742023 1 61 2 33 3 95 4 76a. Do the data exhibit any patterns? Please explain.b.Use an appropriate LINEAR REGRESSION method to forecast the H&CP sales for the first, second, third and fourth quarter of 2024. c.GDC buys each unit of H&CP for $4,500 and pays another $100/unit for transportation. Each unit is sold for $6,200. GDC uses the sum of the four quarterly forecasts for 2024 as the estimate of the mean of the normal distribution describing the annual demand for H&CP. Standard deviation of the distribution is estimated as 15% of the mean. Any H&CP not sold during the year is sold to a contractors’ discount store for $3,900. How many units should GDC order to maximize its expected profits? d.GDC’s VP for procurement suggested that the company should adopt a service level of 0.90 because the Company takes pride in high level of customer service and the long term cost of losing a customer is much more than the profit they would make on a single unit.i.What is the optimal order size associated with 0.90 service level?ii.What is the goodwill cost implied by the 0.90 service level?2. Great Bows (GB) is trying to decide whether to market a new product. As in many new-product situations, there is considerable uncertainty about whether the new product will eventually “catch on.” GB believes that it might be prudent to introduce the product in a regional test market before introducing it nationally. Therefore, the company’s first decision is whether to conduct the test market. GB estimates that the net cost of test market is $50,000. If it decides to conduct the test market, it must then wait for results of the test market. Based on these results, it can then decide whether to market the product nationally. On, the other hand, if the original decision is not to run a test market, then the final decision – whether or not to market the product nationally- can be made without further delay. GB figures that a successful product (in the national market) is worth $1,200,000 whereas a failure will cost the company $500,000. The company wants to use a decision tree approach to find the best strategy. GB’s marketing analyst estimates the following probabilities:Probabilities of test market outcomes: Success: 0.60 Failure: 0.40Probabilities of national market outcomes, given no test market: Success: 0.50 Failure: 0.50Probabilities of national market outcomes, given successful test market Success: 0.70 Failure: 0.30Probabilities of national market outcomes, given failure in test market Success: 0.20 Failure: 0.80Draw a decision tree of GB’s problem and determine the best action and the expected net profit associated with the best action.