Hand calculation will be fine. I need very soon Cup s June 29, 2018, a day befor
ID: 419096 • Letter: H
Question
Hand calculation will be fine. I need very soon
Cup s June 29, 2018, a day before the start of the second stage of the 2018 FIFA World pastries types of pastries, Strudels normal distribution with mean 5,000 units costs $1 to make, in Kazan for $0.5 per pastry. to against Argentina in Kazan, Rusia. A baker is facing the decision on how many n order to maximize its profit during the game. It is planning to sell two different (S) and Croissants (C). Each type of pastry estimated demand follows a and standard deviation 500 units. Each individual pastry and each sells for $5. At the end of the day, any unsold pastries are sold to a baker (a) (4 points) What is the optimal amount of each pastry to stock? The baker conceptualizes a new pooled pastry called Strudessant. Let Ds and Dc be the random variables representing the demands for pastries S and C respectively. Market studies indicate that the demand for the Strudelssant pastry, in the absence of flavors S and C, is simply given by As noted earlier, each of Ds and Dc is normally distributed with mean 5,000 units and standard deviation 500 units. Furthermore Ds and Dc are independent of each other. 4 points) What is the mean and standard deviation of the demand for the Strudelsant pastry?Explanation / Answer
Answer to question 2.a :
Following details are provided :
Cost of each pastry = C = $ 1/ unit
Price for each pastry = P = $ 5/ unit
Salvage price per pastry = S = $0.5 / unit
Therefore ,
Underage cost = Cu = P – C = $5 - $1 = $4 / unit
Overage cost = Co = C – s = $1 - $0.5 = $0.5/ unit
Therefore ,
Critical ratio = Cu / ( Cu + Co ) = 4/4 + 0.5 = 4/4.5 = 0.8888
Critical ratio is the probability of optimum stocking quantity .
Corresponding Z value of probability 0.8888 = NORMSINV ( 0.8888) = 1.22
Therefore ,
Optimum amount of pastry to be stocked
= Mean demand + Z value x Standard deviation of demand
= 5000 + 1.22 x 500
= 5000 + 610
= 5610
OPTIMUM AMOUNT OF EAH PASTRY TO STOCK = 5610 UNITS
Answer to 2b :
Mean demand of Strudelssant pasty
= Mean demand of S + Mean demand of C
= 5000 + 5000
= 10,000 units
Variance of Strudelssant pastry
= Variance of S + Variance of C
= 500 ^2 + 500^2
= 2 x 500^2
Since standard deviation = Square root ( variance ) ,
Standard deviation of Strudelssant pastry
= Square rot ( 2 x 500^2 )
= 500 x Square root ( 2 )
= 500 x 1.4142
= 707.1 ( 707 rounded to nearest whole number )
OPTIMUM AMOUNT OF EAH PASTRY TO STOCK = 5610 UNITS
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