Yak & That ’ ?is a small company that designs, produces, and sells rain jackets and other outdoor apparel. The design team has finalised its new rain jacket design for the coming autumn season. Now it's time to decide how many jackets to produce before the season starts, as no other production runs will be possible once the season begins. Forecasting rain jacket demand months in advance is tricky. ‘ Yak & That ’ ?has only been operating for three years, with varying sales success. Based on past sales, current market conditions, and expert judgment, 1 2 ‘ Yak & That ’ ?employees have independently estimated demand for the new rain jacket design this upcoming season. Their estimates are presented in Table 4 . ?To assist in the decision on the number of units for the production run, management has gathered the data in Table 5 . Table 4 : Estimated Demands ? Table 5 : Monetary Values Variable production cost per unit ( C ) : £ 8 0 Selling price per unit ( S ) : £ 1 0 0 Salvage value per unit ( V ) : £ 3 0 Fixed production cost ( F ) : £ 1 0 0 , 0 0 0 1 4 , 0 0 0 1 6 , 0 0 0 1 3 , 0 0 0 8 0 0 0 1 4 , 0 0 0 5 0 0 0 1 4 , 0 0 0 1 1 , 0 0 0 1 5 , 5 0 0 8 0 0 0 1 0 , 5 0 0 1 5 , 0 0 0 7 Note that S is the price ‘ Yak & That ’ ?charges retailers. Any rain jackets that do not sell during the season can be sold by ‘ Yak & That ’ ?to discounters for V per jacket. The fixed cost of plant and equipment is F . ?This cost is incurred regardless of the size of the production run. a . ‘ Yak & That ’ ?management believes that a normal distribution is a reasonable model for the unknown demand in the coming year. What mean and standard deviation should ‘ Yak & That ’ ?use for the demand distribution? [ 3 ] b . ?Use a spreadsheet model to simulate 1 0 0 0 ?possible outcomes for demand in the coming year. Based on these scenarios, what is the expected profit if ‘ Yak & That ’ ? produces Q = 7 8 0 0 ?rain jackets? What is the expected profit if ‘ Yak & That ’ ?produces Q = 1 2 , 0 0 0 ?rain jackets? What is the standard deviation of profit in these two cases? [ 6 ] c . ?Based on the same 1 0 0 0 ?scenarios, how many rain jackets should ‘ Yak & That ’ ?produce to maximize expected profit? Call this quantity Q . [ 3 ] d . ?Should Q equal mean demand or not? Explain. [ 2 ] e . ?Create a histogram of profit at the production level Q . ?Create a histogram of profit when the production level Q equals mean demand. What is the probability of a loss greater than £ 1 0 0 , 0 0 0 ?in each case? [ 3 ] f . ?In the report, summarise answers to the above questions and discuss any additional insights that would support decision making. PLease provide the exact solution with the values and steps in detailed on how to do it excel by using risk tool.