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Sonbull [250]
3 years ago
14

Find a current example of a linear optimization model used in your industry. Describe the industry's needs, including any unique

factors, how the linear optimization model was used, and the problem or challenge it addressed. Would you suggest a different model be used
Mathematics
1 answer:
marishachu [46]3 years ago
5 0

Answer:

Follows are the explanation to the given question:

Step-by-step explanation:

Its determination of inventory amounts for various products. Its demand is an excellent illustration of a dynamic optimization model used in my businesses. Throughout this case, its store has restrictions within this room are limited. There are only 100 bottles of beverages to be sold, for instance, so there is a market restriction that no one can sell upwards of 50 plastic cups, 30 power beverages, and 40 nutritional cokes. Throughout this situation, these goods, even the maximum quantity supplied is 30, 18, and 28. The profit for each unit is $1, $1.4, and $0.8, etc. With each form of soft drink to also be calculated, a linear extra value is thus necessary.

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John invested $17,500 that
babymother [125]

Answer:

<u>The future value of the investment after 10 years is $ 29,240.53</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Principal = $ 17,500

Interest rate = 5.2% = 0.052 compounded semiannually

Time = 10 years = 20 semesters

2. What is the future value of the investment after 10 years​?

Let's use the formula of the Future Value, to calculate it for this investment:

FV = P * (1 + r) ⁿ

Let's replace with the real values:

FV = 17,500 * (1 + 0.052/2)²⁰

FV = 17,500 * 1.670887521

<u>FV = 29,240.53</u>

6 0
3 years ago
The circumference of a circle is C centimeters. The diameter of the circle is 19 centimeters. Which expression best represents t
sp2606 [1]

Answer:

Step-by-step explanation:

C = 19π

π = C/19

5 0
3 years ago
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If there are 60 sides, what is the difference between the perimeter and π?
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2 years ago
The net best represents which of the solids?
Debora [2.8K]

Answer:

Where is the picture for the question?

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2 years ago
A shop sells a particular of video recorder. Assuming that the weekly demand for the video recorder is a Poisson variable with t
julia-pushkina [17]

Answer:

a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.

b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.

c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.

Step-by-step explanation:

For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}

In which

x is the number of successes

e = 2.71828 is the Euler number

\lambda is the mean in the given interval.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Poisson distribution can be approximated to the normal with \mu = \lambda, \sigma = \sqrt{\lambda}, if \lambda>10.

Poisson variable with the mean 3

This means that \lambda= 3.

(a) At least 3 in a week.

This is P(X \geq 3). So

P(X \geq 3) = 1 - P(X < 3)

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Then

P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}

P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498

P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494

P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240

So

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768

0.5768 = 57.68% probability that the shop sells at least 3 in a week.

(b) At most 7 in a week.

This is:

P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

In which

P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}

P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498

P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494

P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240

P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240

P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680

P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008

P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504

P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216

Then

P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988

0.988 = 98.8% probability that the shop sells at most 7 in a week.

(c) More than 20 in a month (4 weeks).

4 weeks, so:

\mu = \lambda = 4(3) = 12

\sigma = \sqrt{\lambda} = \sqrt{12}

The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.

Z = \frac{X - \mu}{\sigma}

Z = \frac{20 - 12}{\sqrt{12}}

Z = 2.31

Z = 2.31 has a p-value of 0.9896.

1 - 0.9896 = 0.0104

0.0104 = 1.04% probability that the shop sells more than 20 in a month.

5 0
2 years ago
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