Crestview sells a particularly popular Christmas card once a year and distributes the cards to gift shops. It costs Crestview $0.5 per card to order from a printing company, and Crestview receives $1.0 for each card sold. The printing company costs $0.30 to print each card. Because the cards have the current year printed on them, those cards that are not sold are discarded at no value. Crestview has estimated that the demand for the coming Christmas season follows a normal distribution with a mean of 100,000 and standard deviation of 20,000.

a) Determine the optimal number of cards Crestview should order for the coming Christmas season.

b) Suppose Crestview has purchased a printing machine and will print cards themselves. The cost to print each card is still $0.30. Determine the optimal number of cards Crestview should print for the coming Christmas season.

c) Interpret the difference between the results in a) and b).