Question $1(10$ points$)$We plan to prioritize the location of a factory in Windsor area. The following table summarizes different factors that will affect our decision. Assume that the weight of the subjective factors Labor Availability and Business Climate are $0\mathrm{.}8$ and $0\mathrm{.}2,$ respectively. Assume that the weight of the subjective factors are twice more than the weights of the objective factors $(=2*).$ Answer the following questions.Objective Factor Subjective factorsA $11015120\mathrm{.}50\mathrm{.}2$ B $220110350\mathrm{.}60\mathrm{.}7$ C $18095250\mathrm{.}90\mathrm{.}8$a$)$ What are the values for Alpha and Beta? $(2$ Points$)$b$)$ What are the values for OFM$\_$A$,$ OFM$\_$B$,$ and OFM$\_$C$?(3$ Points$)$ c$)$ What are the values for SFM$\_$A$,$ SFM$\_$B$,$ and SFM$\_$C$?(3$ Points$)$ e$)$ Which facility is chosen as the best option? $(2$ Point$)$ Site Revenue in $$1,000$ Energy cost in $$1,000$ Labor cost in $$1,000$ Labor Availability Business Climate $1$Question $2(20$ points$)$A furniture company that provides office desks in Ontario, presently considers renting warehouses among three potential warehouses $($A$,$ B$,$ and C$)$ to serve the customers in Toronto, Hamilton, London, and Windsor. The following table summarizes the average unit transportation cost to each city from each warehouse, the number of demands per year for the desks in each city, and the service capacity and rent cost at each warehouse.Unit costWarehouse Toronto Hamilton London WindsorA $$6\mathrm{.}00789$B $78782,400$ $$10,000$C $89774,600$ $$15,000$ Capacity of warehouses $3,100$Annual Rent cost $$14,000$ # of desks $($demands$)13001000900800$ Assume each city only can be served by one warehouse only. The company would like to determine which warehouse will be rented and how to assign each city to the rented warehouses to minimize total cost.a$)$ Formulate the related Linear Programming model for this problem. $(10$ points$)$ b$)$ Solve the problem with Excel solver and submit your Excel file. $(10$ Points$)$Question $3(25$ points$)$Consider the demand for rock salt used primarily to melt snow. This salt is produced by a firm called Tahoe Salt, which sells its salt through a variety of independent retailers around the Lake Tahoe area of the Sierra Nevada Mountains. In the past, Tahoe Salt has relied on estimates of demand from a sample of its retailers, but the company has noticed that these retailers always overestimate their purchases, leaving Tahoe $($and even some retailers$)$ stuck with excess inventory. After meeting with its retailers, Tahoe has decided to produce a collaborative forecast. Tahoe Salt wants to work with the retailers to create a more accurate forecast based on the actual retail sales of their salt. The sales records for the salt in the past year $(12$ months$)$ has been collected in the table in the next page. The manager wants to use the Holts model with Alpha$=0\mathrm{.}1$ and Beta$=0\mathrm{.}1$ for forecasting the sales in the future. Answer the following questions. $($Only Excel files are accepted for this question$)$a$)$ Calculated the initial values for level and trend $($T$0=?$ And L$0=?)(4$ Points$)$ b$)$ Forecast the demand for periods $1$ to $12.(10$ Points$)$c$)$ Calculate the TS$\_$t factor for periods $1$ to $12$ and determine whether the Holts method is acceptable for this data set or not. $(10$ Points$)$d$)$ What is the expected sale for period $15($F$15=?)?(1$ Point$)2$ Period $($t$)$ Demand $($Dt$)18,000213,000323,000434,000510,000618,000723,000838,000912,0001013,0001132,0001241,000$