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 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?
Answer: - According to given data
Mean = 1200 and standard deviation = 200
Cost price = $1.50 , Seeling price = $5.00 and Salvage price = $0.00
Where formula to calculate optimal order quantity (Q) = Mean + Z * Stanfard deviation
We need to calculate z value formula is critical value = Cu / Cu + Co
Where Cu = underage cost = selling price - cost price = $5.00 - $1.50 = $3.50
Co = overage cost = cost price - salvage price = $1.50 - $0.00 = $1.50
Critical value = $3.50 / ($3.50+$1.50) = $3.50 / $5.00 = 0.70
Where from standard probability table z value for obtained critical value = 0.53
So Optimal quantity = 1200 + 0.53*200 = 1306 copies
A local bookstand believes that the demand for the Olympic edition of a sports magazine is...