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 $0.10 per card, and the cost of printing is $0.25 per card. The company receives $4.15 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 6,200 and standard deviation 150. (Assume these four are independent.)

What is the optimal production quantity for the card? (Use Excel's NORMSINV() function to find the correct critical value for the given -level. Do not round intermediate calculations. Round your answer to the nearest whole number.)

Explanation / Answer

Cost price = Cost of paper + Printing cost = 0.1 + 0.25 = 0.35

Selling price = 4.15

Cost of shortage (Cs) = Selling price - Cost price = 4.15 - 0.35 = 3.8

Cost of excess (Ce) = Cost price = 0.35

Service level = Cs/(Cs+Ce) = 3.8/(3.8+0.35) = 0.92

z value for Service level 0.92 is 1.38

Optimal quantity for each region = Mean + z*standard deviation = 6200 + 1.38*150 = 6407 units

So, for all the 4 regions, total optimal quantity = 4*6407 = 25628 units

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