Number of customers from 4 regions together for Wholemark = 4700 x 4 = 18800 Sta

Question

Number of customers from 4 regions together for Wholemark = 4700 x 4 = 18800

Standard deviation of customers for each region = 480

Hence, standard deviation of customers of 4 regions together =   480 x square root ( 4 ) = 480 x 2 = 960

Cost of card per unit = C = $0.10 + $0.20 = $0.30

Price of card per unit = P = $2.15

Salvage value of card per unit = S = 0 ( unsold cards have no value )

Hence,

Cost of underage = Cu = P – C = $2.15 - $0.30 = $1.85

Cost of overage = Co = C – S = $0.30 – 0 = $0.30

Hence, Critical ratio = Cu/ Cu + Co = 1.85/ ( 1.85 + 0.3) = 1.85/ 2.15 = 0.86

Critical ratio is the probability of the optimum production quantity.

Therefore , Probability = 0.86

And corresponding Z value = NORMSINV ( 0.86 ) = 1.0803

Hence optimal order quantity

= Number of customers from 4 region together + Z x Standard deviation of customers from 4 regions together

= 18800 + 1.0803 x 960

= 18800 + 1039.68

= 19839.68 ( 19840 rounded to next higher whole number )

OPTIMAL PRODUCTION QUANTITY = 19840

OPTIMAL PRODUCTION QUANTITY = 19840

Explanation / Answer

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 $0.20 per card. The company receives $2.15 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 4,700 and standard deviation 480. (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.)

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