Wholemark is an Internet order business that sells one popular New Year's greeting card. The cost of the paper on which the card is printed is $0.10 per card, and the cost of printing is $0.42 per card. The company receives $2.40 per card sold. Since the cards have the current year printed on them, unsold cards have no salvage value. Based on past data, the number of customers from Los Angeles is normally distributed with a mean of 2,500 and a standard deviation 600. What is the optimal production quantity for the card for Los Angeles, if Wholemark only makes a one-time production for this area?

Optimal production quantity = 2970

Explanation:

As per the data given in the question,

Cost of card (c) = $0.10 + $0.42 = $0.52

Selling price (p) = $2.40

Salvage value (v) = 0

So,Critical ratio (Z)

= (p - c) ÷ (p - v)

= ($2.40 - $0.52) ÷ ($2.40 - 0)

=0.7833

Z(0.7833) = NORMSINV (0.7833)

Z(0.7833) = 0.783387

n = no. of city = 1

μ = n × mean demand = 1 × 2,500 = 2,500

Optimal production quantity = μ + Z (0.7833) × standard deviation

= 2,500 + 0.783387 × 600

= 2970.03

= 2970

We simply applied the above formula

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