Problem $20-7($Algo$)$

Wholemark is an Internet order business that sells one popular New Year's greeting card once a year. The cost of the paper on which the card is printed is $$0\mathrm{.}10$ per card, and the cost of printing is $$0\mathrm{.}20$ per card. The company receives $$2\mathrm{.}15$ per card sold. Because the cards have the current year printed on them, unsold cards have no salvage value. Its customers are from the four areas: Los Angeles, Santa Monica, Hollywood, and Pasadena. Based on past data, the number of customers from each of the four regions is normally distributed with a mean of $4,700$ and a standard deviation of $480.($Assume these four are independent.$)$

What is the optimal production quantity for the card?

Note: Use Excel's NORMSINV$()$ function to find the correct critical value for the given $-$level. Do not round internfediate calculations. Round Normsinv value to $4$ decimal places. Roundup your answer to the nearest whole number.

Optimal production quantity