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3 years ago

7

Lou wants to make a coffee mixture to sell. He is going to mix Sumatra coffee which costs $2.50 per pound with Columbian coffee

which costs $3.75 per pound. He wants to male 50 pounds of mix and he wants the cost of the mix to be $3.35 per pound. How many pound of each will he need?

1 answer:

Scilla [17]3 years ago

5 0

To answer this question you need to create 2 equations:
S+C=50
2.50S+3.75C=3.35*(50)
S=50-C -so now you can plug in S into the second equation
2.50*(50-C)+3.75C=167.5
Now you just need to solve this equation, the final answer will be 34 pounds of colombian coffee and 16 pounds of sumatra coffee

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Step-by-step explanation:

So the triangle who posses the angle with measurement k=35 is an isosceles. I know this because there are two congruent legs. Those 2 congruent legs tell us the angles opposite of them are all congruent.

So we know one equation to solve is:

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3 years ago

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

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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.

Answer:

a

$N = 46728$

b

$n = 47728$

c

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

$z = 0$

So

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

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Answer:

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Step-by-step explanation:

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