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Problem $11-7($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 $$0\mathrm{.}45$ per card, and the cost of printing is $$0\mathrm{.}15$ per card. The company receives $$5\mathrm{.}00$ per card sold. Since 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 $3,500$ and a standard deviation $350.($Assume these four are independent.$)$

What is the optimal production quantity for the card?

Note: Use Excel's NORM.S$.$INV$()$ function to find the z value. Round $z$ value to $2$ decimal places. Round your answer to the nearest whole number.

Optimal production quantity