Bella's stocks and sells the X-model fans in the summer and the demand is normally distributed with mean 100 and standard deviation 25. Bella's makes a one-time purchase of the fans prior to the summer at a cost of $40 each and sells them for $60 each. Any fans unsold at the end of summer are marked down to $29 and sold in a special fall sale. Assume that all the marked-down fans are sold.

1. 1. How many fans should Bella'spurchase at the beginning of summer. (answer should be 109)
   2. Compute the fill rate resulting from this stocking policy? What is the expected profit? (answer should be 93.89%, 1711.59)
   3. Bella's is considering reducing the sales price to $55 and expects that as a result of this change, the mean demand will increase to 140. Determine whether they should pursue this strategy. Assume that the coefficient of variation of demand remains the same. (answer should be 1743.76)

Please show the calculations. The final answers are in the parentheses