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2 years ago

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write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind o

nly 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step

1 answer:

nekit [7.7K]2 years ago

7 0

Answer:

Plane speed = 40 m/s.

Wind speed = 300 m/s.

Step-by-step explanation:

Let the speed of the plane = Y

And the speed of the wind = X

If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,

X + Y = 340 ..... ( 1 )

Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,

X - Y = 260 ..... ( 2 )

Solve the two equations simultaneously by addition. That will eliminate Y

X + Y = 340

X - Y = 260

2X = 600

X = 600/2

X = 300 m/s

Substitutes X in equation (1)

300 + Y = 340

Make Y the subject of formula by collecting the like terms

Y = 340 - 300

Y = 40 m/s

Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.

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2 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

4 0

2 years ago