Mathematics, 09.12.2020 21:20 wiltseliz4800

Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017). a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?
b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma. com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.
c. Please state whether the following statement is always true, and give a brief explanation. If c=c, the newsvendor solution is the mean.

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Answer from: alexciamartinez05

Complete Question

Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017).

a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?

b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma.com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.

c. Please state whether the following statement is always true, and give a brief explanation. If C_o =C_i , the news vendor solution is the mean.

N = 46728

n = 47728

Yes it is always true

Step-by-step explanation:

From the question we are told that

The regular price of the jersey is $P_r = \$ 80$

The cost of producing a jersey is $C= \$ 40$

The left-over price of the jersey is P_o = $ 30

The mean is $\mu = 40000$

The standard deviation is $\sigma = 8000$

The cost of lost customer goodwill is $C_g = \$ 10$

Generally the fund that LCF will loss for one jersey if they order for too many jersey (i.e more than they need )is mathematically represented

C_o = P_o - C

=> C_o = 40 - 30

=> $C_o = \$ 10$

Generally the fund that LCF will loss for one jersey if they order lesser amount jersey (i.e less than they need )is mathematically represented

C_i = P_r - C

=> C_i = 80 - 40

=> $C_i = \$ 40$

Generally the critical ratio is mathematically represented as

$Z = \frac{C_i }{ C_i + C_o}$

=> $Z = \frac{40}{ 40 + 10}$

=> Z = 0.8

Generally the critical value of Z = 0.8 to the right of the normal curve is

z = 0.841

Generally the optimal quantity of jersey to order is mathematically represented as

$N = \mu * [z * \sigma]$

=> N = 40000 * [0.841 * 8000]

=> N = 46728

Considering question b

Generally considering the factor of customer goodwill the fund that LCF will loss for one jersey if they order lesser amount jersey (i.e less than they need )is mathematically represented as

C_k = C_i + C_g

=> C_k = 40 + 10

=> $C_k = \$ 50$

Now the critical ratio is mathematically represented as

$Z = \frac{C_k }{ C_k + C_o}$

=> $Z = \frac{50}{ 50 + 10}$

=> Z = 0.833

Generally the critical value of Z = 0.833 to the right of the normal curve is

z = 0.966

Generally the optimal quantity of jersey to order is mathematically represented as

$n = \mu * [z * \sigma]$

=> n = 40000 * [0.966 * 8000]

=> n = 47728

Considering question c

When C_o =C_i then

The critical ratio is mathematically represented as

$Z = \frac{C_k }{ C_k + C_k}$

=> $Z = \frac{1}{ 2}$

=> Z = 0.5

Generally the critical value of Z = 0.5 to the right of the normal curve is

z = 0

The optimal quantity of jersey to order is mathematically represented as

$n = \mu * [z * \sigma]$

=> n = 40000 * [0* 8000]

=> $n = 40000 = \mu$

Hence the statement in c is true

Answer from: Quest

this might get deleted, sorry. it has to be an actual question. if you really wanted to give someone free points, ask a question like "why does the sky look blue, and the sun is yellow to our eyes? "

step-by-step explanation:

Answer from: Quest

8121 because

130,000 divided by 16 is 8121

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Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The...

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