A company is trying to determine how many Valentine’s Day cards to produce. The cost of printing x cards is $2 million +0.70x. F
or example, printing 1 million cards costs $2.7 million. Weekly demand for cards follows a normal random variable with a mean of 1.5 million and a standard deviation of 200,000 for a week before the day and a normal random variable with a mean of 0.5 million and a standard deviation of 300,000 for the week before that. The cards are sold for $4.00, and leftover cards have a value of $0.05. With the precision of 0.2 million, determine how many cards should the company produce to maximize its profit.
