Wholemark is an Internet order business that sells one popular New Year greeting

Question

Wholemark is an Internet order business that sells one popular New Year greeting card once a year. The cost of the paper on which the card is printed is $0.45 per card, and the cost of printing is $0.15 per card. The company receives $5.00 per card sold. Since the cards have the current year printed on them, unsold cards have no salvage value. Their 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 mean 3, 500 and standard deviation 350. (Assume these four are independent.) What is the optimal production quantity for the card? (Round your answer to the nearest whole number.) Optimal production quantity

Explanation / Answer

Cost of underestimating the demand (Cu) = 5 - (0.45 + 0.15) = $4.4

Cost of overestimating the demand (C0) = 0.45 + 0.15 = $0.60

So,

Optimal probability that the card is not being sold

P = 4.4 / (4.4 + 0.6)

P = 0.88

z value corresponding to p = 0.88 is 1.175.

Hence,

Optimal production quantity

= 3500 + 1.175(350)

= 3911 (Rounded off to the nearest whole number)

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