This problem will be solved using Newsvendor model Here, Price for target = P =
ID: 374353 • Letter: T
Question
This problem will be solved using Newsvendor model
Here,
Price for target = P = $ 190/ unit
Cost for target = C = $170/ unit
Salvage value/ unit = S = 0.70 X 190 ( since it is salvaged at 30% discount) = $133
Hence,
Underage cost = Cu = P – C = 190 – 170 = 20
Overage cost = Co = C – S = 170 – 133 = 37
Hence, Critical ratio = Cu/ ( Cu + Co) = 20 / ( 20 + 37 ) = 20/57 = 0.3508
Critical ratio is the probability of demand corresponding to the optimum quantity which maximizes profit
Therefore, Z value corresponding to probability 0.3508 = NORMSINV ( 0.3508) = - 0.38316
Hence, Number of books to be ordered
= Mean demand + Zvalue x Standard deviation of demand
= 100 - 0.38316 x 42
= 100 - 16.09
= 83.91 ( 84 ROUNDED TO NEXT HIGHER WHOLE NUMBER )
NUMBER OF X BOX TO BE ORDERED TO MAXIMIZE PROFIT = 84
NUMBER OF X BOX TO BE ORDERED TO MAXIMIZE PROFIT = 84
Explanation / Answer
2. Target is trying to decide on how many units of Xbox one S to purchase for the holiday season. One unit of Xbox one S retails at $190.00. Microsoft, manufacturer and supplier of the Xbox one S to B&N sells a unit to Target for $170.00. Target will dispose of all of the unsold units of the Xbox one S at 30% off the retail price, at the end of the season. Target estimates that demand for this book during the holiday season is normally distributed with a mean of 100 and a standard deviation of 42. a. How many units of Xbox one S should Target order to maximize his expected profit?
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