2. A cosmetics manufacturer is deciding between two chemical formulas Fermat Aar Formula B - from which to make a new Itpstsck. Formula A is tors costly to manufacture than Formula B but contains on ingredient that is more likely to cause Itstrs a slight allergic reaction than are the ingredients an Formula B. Using Formula A instead of formula B would reduce production costs by SI mullion a year regardless of the volume of lipstick manufactured and sold that year, but would cause an alkrgic reaction in 3 polecat of all mos. Using Fortnula B would cause an allergic reaction in 1 percent of all users. The MAR claim the manufactuto must pay because of each allergic (0701011 is $250.

a. If 100.000 persons a yeas use the new lipstick. Mal et the annual expected value of allergic reaction claims the manufacturer must my

i. Formula A is used: Show your calculations.

ii. Formula B as used? Show your calculations.
b. On the basis of information rind your answer to (a). will use of Formula A result in lower annual total cads (including the ant of allemtc rev lion daunts) than use of Faunas B it

i. 100,000 persons use the lipstick each year? Show )our calculation.

ii. 500.000 portions use the lipstick each reel Show your calculations.

3. ABC Inc. has the total imentoo of 510,000. Currently. ABC has this entire inventory stored in one warehouse. There is a 5% chance that a lire could occur. If this fire occurs, then ARC will lose their entire, ;monetary. (Option Al As an alternative to keeping their entire inventory in one warehlane. ARC is miss:tering separating their inventory evenly into two different warehouses. Once again, there is a 5% chance that a fire could occur in each warehouse. If this fire occurs. then ABC

would once again lawa their enure inventory in that particular warehouse. iription Given the following. should ADC implement Option B? Why or why not?
Option A OplIon B
Mean 500 500
Standard Deviation 2179A5 1541.10
Coefficient of Variation 4.36 3.05