The Highland Company is planning orders for its winter catalog. One order is to be placed at the beginning of the season. The demand forecast for one of its jackets is normally distributed, with a mean of 5,000 and standard deviation of 2,000. Each jacket is purchased for $100, and any unsold jackets at the end of the season will be discounted and sold through the outlet store for $75. At this price, virtually all jackets are expected to sell. It costs another $15 to store an unsold jacket for the season and then move it to the outlet store. The members of the buying committee disagree on the effect of stocking out and the number of jackets to be ordered. One of the members believes that 6,000 jackets should be ordered, whereas another wants to order 8,000 jackets.
a. At what cost of stocking out would each member’s order size be justified?
b. If the planned sale price is $200, describe a situation in which ordering 6,000 jackets makes sense. Describe another situation in which ordering 8,000 jackets makes sense.