Problem
Cap Inc. is a manufacturer of masks, hats, and wigs. A team of experts met to forecast what can sell well for the Halloween this year. One product that was high on their list is a realistic 3D face mask, which they call Full-Face Old. Full-Face Old is produced in Vietnam, so they made a single order well ahead of time for the upcoming Halloween. The team estimated that the demand for Full-Face Old follows a Normal distribution with mean 900,000 and standard deviation of 4000. They entered negotiations with their Vietnamese manufacturer, and it gave them an offer of $6 for each mask, and $2 for any unsold mask returned to them. Cap Inc. has decided to sell each mask for $19 in the market. They also need to pay $1 to a local warehouse to hold the unsold masks after the event (left-overs) so that the Vietnamese manufacturer pick them up later.
i. How many Full-Face Old masks should Cap Inc. order?
ii. If Cap Inc. orders 905,000 masks, what will be their service level?
iii. If Cap Inc. orders 905,000 masks, how many sales of masks are they expected to lose on the event?
iv. Assume that Cap Inc. orders 904,000 masks, how many masks will they expect to send to the local warehouse after the event?