A local bookstand believes that the demand for the Olympic edition of a sports magazine is normally distributed with a mean of 1,200 and a standard deviation of 200. Each copy of the magazine costs the bookstand $1.50 per copy, and the bookstand will sell the issue for $5.00. Following the Olympic Games, there will be no demand for the magazine, and all leftover copies will be recycled because they will have no salvage value. What is the optimal number of copies of the Olympic edition that the bookstand should order?

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Tundexigo Tundexigo · Answer 1

Answer:

1,304 copies

Explanation:

Overage cost (Co) means like cost of over ordering

Co = Cost price - Salvage value

Co = $1.50 - $0 (No salvage value)

Co = $1.50

Underage cost (Cu) means like cost of under ordering

Cu = Selling price - Cost price

Cu = $5.00 - $1.50

Cu = $3.50

Service level = Cu / (Cu + Co)

Service level = $3.50 / ($3.50 + $1.50)

Service level = $3.50 / $5.00

Service level = 0.7

Z-value = NORMSINV (Service level), Using Ms Excel

Z-value = NORMSINV (0.7)

Z-value = 0.52

Optimal Order Quantity (Q) = Mean Demand + (Z-value*Standard deviation)

Optimal Order Quantity Q = 1,200 + (0.52*200)

Optimal Order Quantity Q = 1,200 + 104

Optimal Order Quantity Q = 1,304 copies