linear programming word problems

Let us solve linear programming word problems

Let us take 2 variables x and y to represent the number of chairs & tables respectively.
Hence the price of x tables = 1200x & the price of y chairs = 500y.
Here the total investment cannot be more than 50,000, therefore,
The total price = 1200x + 500y ≤ 50,000. This is the 1st constraint inequality.
Here, hence the storage capacity is for 100 pieces, we have x + y ≤ 100. This is the 2^nd constraint equation. Hence the number of chairs & the number of tables non-negative, we have x ≥ 0, y ≥ 0.
Now, profit on y chairs = 75y. & the profit on x tables is 180 xs
Here, the objective is to maximize the profit, so the objective function is 180x + 75y.
Hence the linear programming model is given by:
Maximize Z = 180x + 75y
Subject to the constraints
1200x + 500y ≤ 50,000
x + y ≤ 100
x ≥ 0, y ≥ 0.

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poisson distribution table

Let us learn about poisson distribution table

The number of successes in a Poisson experiment is said to be as a Poisson random variable. A Poisson distribution is referred as a probability distribution of a Poisson random variable.

Best example of Poisson distribution table

The number of alpha particles emanated by a radio-active source in a specified time interval.

The number of mobile calls received at a telephone exchange in a mentioned time interval.

The Poisson distribution is an another discrete probability distribution

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probability equations

Let us learn about probability equations

Probability is referred as the branch of mathematics which studies the possible outcomes of given events together with the outcomes' relative likelihoods & distributions. In common usage, the word "probability" is applied to mean the chance that a particular event or set of events will occur expressed on a linear scale from “0” impossibility to 1 certainty, also expressed as a percentage between 0 & 100%. The analysis of events governed by probability is known as statistics.

In a class of sixty students, ten are in the drawing club & fifteen are in the games club. If a learner is selected randomly, what is the probability that the selected learner is:
a) In the drawing club?
b) In the games club?
Probability Equations Solution:
The total number of learner in the class = 60
Number of learners in the drawing club = 10
Number of learners in the games club = 15
The probability of solving that the selected learners in the drawing club is,
P (students in drawing club) = 10 / 60
= 1/6
= 0.17
The probability of solving that the selected learner in the games club is,
“P” students in games club) = 15 / 60
= ¼ = 0.25

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frequency distribution table

Let us learn about frequency distribution table
Frequency distribution table is a tabulation of the values that 1 or more variables take in a sample. Each entry in the frequency distribution table contains the frequency or count of the occurrences of values within a particular group or interval, & in this way the table summarizes the distribution of values in the sample.
Frequency distribution table is used to rank the disorganized data from the highest to the lowest. A frequency distribution table is an organized tabulation of the number of individual scores located in each category on the scale of measurement. Frequency distribution table contains at least 2 columns – 1 for the score categories (X) & another for the frequencies (f).
Frequency distribution table can be represented in a number of ways.
Group frequency table as Regular frequency table
Group frequency graph as Polygon; The bar graph; Pie Chart; Histogram
The bar graph is used only when the data or measurements are from a nominal or an ordinal scale. Histogram - Interval or Ratio data, Polygon - Interval or Ratio data

Group frequency distribution table is used when the original scale of measurement consists of more categories which can be listed in a regular table, 20 or more categories is generally considered too much. The easiest & the most complete way to present a set of N= 7 scores is to list each individual score.

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length of arc

Let us learn about length of arc

The arc length “L” is either infinite or finite. If L < ∞ then we can say that C is rectifiable, & is non-rectifiable otherwise. Such description of arc length does not require that C is defined by a differentiable function. The perception of differentiability is not defined on a metric space. The definition of Length of arc for the curve is analogous to the definition of the total variation of a real-valued function. Length of arc is the measure of the distance along the curved line making up the arc. Length of arc is longer than the straight line distance between its endpoints. Length of arc is the fractional part of the circumference subtended by the arc in a circle.

Length of arc = measure of arc × π × d, where d is the diameter of the circle.

360

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factors of 45

Let us learn about factors of 45

45 numbers is a composite number; 45 has factors other than one & itself. 45 is not a prime number.

The 6 factors of 45 are 1, 3, 5, 9, 15, & 45.

The factor pairs of 45 are 1 x 45, 3 x 15, & 5 x 9.

The proper factors of 45 are 1, 3, 5, 9, & 15 or if the definition you are using excludes 1, they are 3, 5, 9, & 15.

The prime factors of 45 are 3, 3, & 5.

There is repetition of these factors, therefore if the prime factors are being listed instead of the prime factorization, usually only the distinct prime factors are listed.

The 2 distinct prime factors of 45 are 3 & 5.

The prime factorizations of 45 are 3 x 3 x 5 or, in index form 3² x 5.

There cannot be common factors, a least common multiple of a single number or a greatest common factor because "common" refers to factors or multiples that 2 or more numbers have in common.

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log identities

Let us learn about log identities

An integer base or number base is the power or exponent to which the base must be raised in order to provide that number is said to be as natural log identities. Real-valued function of a real variable also applied the natural log identities. Inverse function of the exponential function is applying natural logarithm function.
The log identities are written as:
log_ex or ln x
Where e = 2.71828182846.
The Best Example of log identities
In that case we need to apply the addition law of natural logarithms,
Such as, log_eA + log_eB = log_e (A x B).
1. Solve the log identities problem using natural log identities, given ln(4 x 4) =?
Given problem is here to, ln (4x4)
Log identities for the given problem is, ln (x * y) = (ln x) + (ln y).
ln (4 x 4) = ln4 + ln4
Plug the ln2 and ln4 values in the log identities, = 1.386 + 1.386
Then add the values,
= 1.386 + 1.386 = 2.772 = (2 x 4) = 2.772.
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