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 $$0\mathrm{.}80$ per card, and the cost of printing is $$0\mathrm{.}30$ per card. The company receives $$3\mathrm{.}10$ 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 $7,750$ and a standard deviation $100.($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