Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5,000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

Required:
a. For each tire sold, what is the expected cost of the promotion?
b. What is the probability that Grear will refund more than $50 for a tire?

Cadbury has a chocolate factory in dunedin, new zealand. for easter, it makes two kinds of “easter eggs”: milk chocolate and dark chocolate. it cycles between producing milk and dark chocolate eggs. the table below provides data on these two products. demand (lbs per hour) milk: 500 dark: 200 switchover time (minutes) milk: 60 dark: 30 production rate per hour milk: 800 dark: 800 for example, it takes 30 minutes to switch production from milk to dark chocolate. demand for milk chocolate is higher (500lbs per hour versus 200 lbs per hour), but the line produces them at the same rate (when operating): 800 lbs per hour. a : suppose cadbury produces 2,334lbs milk chocolate and 1,652 lbs of dark chocolate in each cycle. what would be the maximum inventory (lbs) of milk chocolate? b : how many lbs of milk and dark chocolate should be produced with each cycle so as to satisfy demand while minimizing inventory?