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 $0.55 per card, and the cost of printing is $0.20 per card. The company receives $3.45 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 6,000 and standard deviation 350. (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 α-level. Do not round intermediate calculations. Round your answer to the nearest whole number.)

  Optimal production quantity

Answer 1

Cost per card = 0.55 + 0.20 = $ 0.75

Selling price per card = $ 3.45

Salvage value per card = 0

Understocking cost (Cu) = Selling Price - Cost = 3.45 - 0.75 = $ 2.7

Overstocking cost (Co) = Cost - Salvage value = 0.75 - 0 = $ 0.75

Critical ratio = Cu / ( Cu + Co) = 2.7 / ( 2.7 + 0.75) = 2.7 / 3.45 = 0.7826

Z value for 0.7826 = 0.7810 ( Using NORMSINV() function in MS Excel)

Combined mean for the 4 locations = 6000 x 4 = 24000

Combined standard deviation for the 4 location = √ ( ( 350^2) + ( 350^2) + ( 350^2) + ( 350^2))  

= √ 490000 = 700

Optimal Production Quantity = Mean + ( Z x Standard Deviation)

= 24000 + ( 0.7810 x 700)

= 24000 + 546.7

= 24546.7