1. Crestviewsells a particularly popular Christmas card once a year anddistributes the cards to gift shops. It costs Crestview $1 per cardto order from a printing company, and Crestview receives $2 foreach card sold. Each card that is not sold is discarded, andCrestview receives $0.1 for each.Crestview has estimated that the demand for the coming Christmasseason follows a normal distribution with a mean of 100,000 andstandard deviation of 30,000.

a)Determine theoptimal number of cards Crestviewshould order for the comingChristmas season.

b)SupposeCrestview has purchased a printing machine and will print cardsthemselves. The cost to print each card is $0.75.Determine theoptimal number of cards Crestviewshould print for the comingChristmas season.

c)Interpretthe differencebetween the results in a) and b).

2. Consider thefollowing information on an inventory managementsystem:

​​ItemCost:​​​$10

​​OrderCost:​​​$300

​​AnnualHolding Cost:​​30% ofitem cost

​​AnnualDemand:​​15,000units based on 300 working days

​​AverageDemand:​​50units

​​Std.Dev. of Demand:​​12unitsperday

​​Leadtime:​​​16days​

a)Ignoring theuncertainty in the demand (i.e. looking only at average values),find the optimal order quantity and the reorder point. What is theannual inventory holding and ordering cost for thispolicy?

b)Consider nowthe uncertainty. The order quantity remains the same. If the targetis to have a 99%fillrate, what shouldbe the reorderpoint? What is thesafety stock? How much additional inventory cost is incurred due tothe safety stock? What should be the reorderpoint?