Planta is deciding how many units to order of their new parka (The Snow maggedon II) for 2020 to be sold through specialty stores. They expect to sell to the retailers 3000 units with a standard deviation of 900 units and have assumed a normal distribution for the demand. The selling price to the retailers is $450. The production cost is $280. Units that are not purchased in Canada will be sold in South America during July where retailers will only pay $250 per unit.

a) Planta quotes an in-stock probability of 90% when placing their optimal order. At how much do they value the cost per unit of unsatisfied demand? Is this equal to the margin made on each parka? Why?

b) Given the quoted in-stock probability of 90%, what is the fill rate Planta offers this parka?

c) Given the quoted in-stock probability of 90%, what is the leftover inventory that Planta should expect for this parka?

d) Now suppose that the product will flop and demand will be zero with some probability p. Alternatively, with probability (1-p) the product will succeed and demand will be normally distributed with a mean of 3000 and standard deviation of 900 units. In this context, Planta orders 4035 units. What is the probability that the product will flop?