Finnish Furniture manufactures tables in facilities located in three cities--Reno, Denver, and Pittsburgh. The tables are then shipped to three retail stores located in Phoenix, Cleveland, and Chicago. Management wishes to develop a distribution schedule that will meet the demands at the lowest possible cost. The shipping cost per unit from each of the sources to each of the destinations is shown in the following table:
To
From Phoenix Cleveland Chicago
Reno 10 16 19
Denver 12 14 13
Pittsburgh 18 8 12
The available supplies are 130 units from Reno, 200 from Denver, and 160 from Pittsburgh. Phoenix has a demand of 140 units, Cleveland has a demand of 160 units, and Chicago has a demand of 200 units.
1. How many units should be shipped from each manufacturing facility to each of the retail stores if cost is to be minimized?
2. What is the total cost?
To minimize costs, the optimal distribution schedule for Finnish Furniture would involve shipping 130 units from Reno to Phoenix, 20 units from Denver to Cleveland, and 160 units from Pittsburgh to Chicago. This allocation is determined by using the transportation algorithm, specifically the Vogel's Approximation Method (VAM), which considers the lowest shipping costs per unit for each source-destination combination. By following this approach, the total cost for the distribution is calculated to be $4,360.
To determine the optimal distribution schedule that minimizes costs, we need to allocate the available supplies from the manufacturing facilities to the retail stores based on the shipping costs per unit. We can achieve this by employing the transportation algorithm, such as the North-West Corner Rule or the Vogel's Approximation Method (VAM).
Using VAM, we begin by identifying the lowest shipping cost per unit for each row and column in the given table. We then select the highest difference between the two lowest costs, considering both rows and columns. This difference indicates the most cost-effective allocation.
In this case, the VAM suggests shipping 130 units from Reno to Phoenix since the shipping cost per unit is 10, which is the lowest for the Reno row. For Cleveland, Denver has the lowest cost at 14, so we allocate 20 units from Denver to Cleveland. Lastly, we allocate 160 units from Pittsburgh to Chicago, as the cost per unit is the lowest at 12 for the Pittsburgh column.
Now, let's calculate the total cost. The cost of shipping 130 units from Reno to Phoenix is 130 x 10 = $1,300. Shipping 20 units from Denver to Cleveland costs 20 x 14 = $280. Lastly, shipping 160 units from Pittsburgh to Chicago costs 160 x 12 = $1,920. Adding these costs together gives us a total cost of $1,300 + $280 + $1,920 = $4,360.
Learn more about Optimal distribution
brainly.com/question/15700934
#SPJ11
Reflect the function f(x) = x4 about the x-axis and translate it 3 units to the left to produce g(x). Which equation represents the function g(x)?.
When f(x) = x⁴ is reflected about the x-axis and translated 3 units to left we get y = -(x - 3)⁴.
Therefore, g(x) = -(x - 3)⁴.
When a function, f(x) is reflected about the x-axis, we get y = -f(x). Therefore here when f(x) = x⁴ is reflected about the x-axis we get y = -x⁴.
When a function, f(x) is translated by a units to the left we get y = f(x-a).
Thus here we obtain y = -(x - 3)⁴
To know more on translation of graph
https://brainly.com/question/12951849
#SPJ4
If 25% of a number is 90 and 70% of the same number is 252, find 95% of that number.
Based on the information provided, 95% of the number is equivalent to 342.
How to find the number?To find the 95% of the number, let's use the rule of three with the information provided to find the 100%.
25% = 90 100% = xBased on this, let's create a simple equation:
x = 100 x 90 / 25 = 360Therefore, 100% of this number is 360, now using this information, let's find the 95% of the same number.
360 / 100 x 95 = 342You can double check this result using the 70% as follows
360/100 x 70 = 252Learn more about equation in: https://brainly.com/question/29657983
Vertical Stretches and Compressions
Answer:
(What roles should the world community and the UNO play to prevent destructive wars in the days ahead in the pretext of the lesson learned from untold loss from the Second World War? Write.)
What are the answers for all 6 100 points
Answer:
Didn’t get it all
Step-by-step explanation:
1
a = x is 6 y is 4
b= x is 2 y is 8
2
a = x is -1 y is 4
b= x is 6 y is 5
3
a x is 5 y is 2
b x is 5 y is 4
4
a x is 6 y is 1
5
a x is 1 y is 1
6
a x is 1 y is 1
plsss help i’ll give brainliest if you give a correct answer
Answer:
x = 23
Step-by-step explanation:
I hope this helps! Have a good day! :)
Solve for Quadratic Equations
10x2 + 20x− 71 = 9
Answer:
x=2 or x=-4. You can also write it as x=2,-4
Step-by-step explanation:
Write your equation and start by subtracting 9 from both sides
10x^2+20x-71-9=9-9
You should end up with
10x^2+20x-80=0
For this equation: a=10, b=20, c=-80
Now we use the quadratic formula and substitute the information. I have attached a picture for you.
which of the four statements are false?
Answer:
D. all atoms are the same
Even though two atoms are chemically identical and might even chemically react in the same way, they are not completely the same to each other
Let f (x) = αx−α−1 for x ≥ 1 and f (x) = 0 otherwise, where α is a positive parameter. Show how to generate random variables from this density from a uniform random number generator
The random variable from of the function f (x) = αx−α−1 for x ≥ 1 and f (x) = 0, where α is a positive parameter is X = (1 - U)^(-1/α).
Explanation; -
Generate random variables from the given density function f(x) = αx^(-α-1) for x ≥ 1 and f(x) = 0 otherwise, using a uniform random number generator, you can follow the inverse transform method. Here are the steps:
1. Find the cumulative distribution function (CDF) F(x) by integrating f(x) with respect to x:
F(x) = ∫f(x)dx = ∫αx^(-α-1)dx from 1 to x, which yields F(x) = 1 - x^(-α).
2. Set F(x) equal to a uniformly distributed random variable U (0 ≤ U ≤ 1):
U = 1 - x^(-α).
3. Solve for x to find the inverse of the CDF F^(-1)(U):
x = (1 - U)^(-1/α).
4. Generate random variables by plugging in uniformly distributed random numbers (from a uniform random number generator) into F^(-1)(U):
X = (1 - U)^(-1/α).
By following these steps, you can generate random variables from the given density function using a uniform random number generator.
To know more about "random vaiable" click here:
https://brainly.com/question/30789758
#SPJ11
DaCN
NOU
Actions E
1
2.
✓ Check
Question 5
Indicate the answer choice that best completes the statement or answers the question,
Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary.
3
4
5
6
7
How high is the ramp?
8
21 ft
h ft
19 ft
Oah? + 192 = 21°: 80 ft
Ob. ha + 192 = 212: 8.9 ft
Och + 19 = 21; 2 ft
Od 212 + 192 = h2,28.3 ft
A regular polygon has 30 sides.
Find the size of each of its exterior angles.
Answer:
12°Step-by-step explanation:
One interior angle in a regular triacontagon is 168 degrees
so
180 - 168 = 12°
X-9 = -27
2
0-24
0-12
11
O 12
______________________________
Hey!!
Solution,
x-9=-27
or, X= -27+9
x=-18
So the value of X is -18
hope it helps..
Good luck on your assignment
__________________________
what graph passes the vertical line test?
X=8,y = 10 find y when x = 68
Answer:
85
Step-by-step explanation:
x:y
8:10
68:y
divide 68 by 8 u get 8.5 and the times it by 10
so y equals 85
if ₱60,000.00 was deposited in a bank and became ₱61,625.00 at the end of 150 days, find the interest rate using exact and ordinary days.
Days exactly: The rate of interest is 4.17%. The interest rate of amount is 4.21% on regular days.
I = P x R x T/365, where I is the interest, P is the principal, R is the rate, and T is the duration, can be used to determine the interest rate using exact days.
I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows: 625 = 60000 x R x 150/365. By multiplying both sides by 365/150, we may find R. As a result, R = 625 x 365/90000 = 4.17%.
I = P x R x T/360, where I is the interest, P is the principal, and R is the rate of return, can be used to get the interest rate using regular days.T stands for time, and R represents the rate. I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows:
625 = 60000 x R x 150/360. By dividing both sides by 360/150, we may find R. As a result, R = 625 x 360/90000 = 4.21%.
I = P x R x T/365, which means that R = I x 365/P x T = 625 x 365/60000 x 150 = 4.17%. Exact days
I = P x R x T/360 on typical days, which means that R = I x 360/P x T is 625 x 360/60000 x 150, or 4.21%.
Learn more about amount here
https://brainly.com/question/28970975
#SPJ4
By what factor would you need to change the radius of a sphere, such that its volume increased by a factor of 7? Please include step by step calculations!
The factor by which radius of the sphere be changed is 1.91, which is calculated by applying the concepts of surface area and volume on the assigned problem.
What do you mean by volume?
Volume is defined as the 3D measurement that deals with the amount of space required by an object. It is always calculated in cubic units. Its basic unit is cubic metre.
Calculation of the change in radius of sphere when its volume is increased by 7Let the radius and volume of sphere be r and v respectively
Volume of sphere, v = 3.16 × ( r )3 —- 1
Now, changed radius, R = xr
Where x is the factor, we need to calculate
Changed volume, V = 7v = 3.16 × ( R )3 -— 2
From equations 1 and 2, we get,
7v / v = ( R )3 / ( r )3
7 = ( xr )3 / ( r )3
7 = (x)3 × 1
Taking cube root both sides,
x = 1.913
Hence, the factor by which radius of the sphere be changed is 1.91.
To learn more about volume, visit the link:
brainly.com/question/463363
#SPJ4
DUE TODAY PLEASE HELP!!!!
For which angles is the cosine positive? Select all that apply.
a
0 radians
b
5π/12 radians
c
5π/6 radians
d
3π/4 radians
e
5π/3 radians
Step-by-step explanation:
if it is between 0 and pi/2 (90°), or between 3pi/2 (270°) and 2pi (360°).
for angle = 0, cos = 1. therefore, positive.
0 <= 5pi/12 <= pi/2. therefore, positive.
pi/2 <= 5pi/6 <= pi. therefore, negative.
pi/2 <= 3pi/4 <= pi. therefore, negative.
3pi/2 <= 5pi/3 <= 2pi. therefore, positive.
you do know how to compare fractions, right ?
you need to bring then to the same denominator by multiplying numerator and denominator by the same factor.
e.g. comparing 5pi/12 with pi/2.
to bring them both to .../12, we have to multiply pi/2 by 6/6.
so, we are comparing 5pi/12 and 6pi/12.
and we see, 5pi/12 is smaller.
the others work the same way.
3pi/6 <= 5pi/6 <= 6pi/6
2pi/4 <= 3pi/4 <= 4pi/4
9pi/6 <= 10pi/6 <= 12pi/6
now you see it clearly.
1. Solve for x in the equation; 3 base x + 34 base x- 40
2. Given that 221 base x =25 base 10, find the base x
Answer:
1 . 40 - 34 equals 14
only can give you number 1 but I hope it jelps
Let A be the event that a student is enrolled in an accounting course, and let S be the event that a student is enrolled in a statistics course. It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and accounting. Find the probability that a student is in accounting and is also in statistics. \begin{tabular}{||l|l|} \hline \hline 0.70 \\ 0.55 \\ 0.12 \\ 0.15 & 0.60 \\ \hline \end{tabular}
The correct option is (E) 0.15 or 15%.
It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and accounting.
The Venn diagram below shows the proportion of students who are enrolled in accounting (A) and statistics (S).
Therefore, from the Venn diagram, the probability that a student is in accounting and is also in statistics is 0.15 (or 15%).
Therefore, P(A ∩ S) = 0.15.
Learn more about Venn diagram from:
https://brainly.com/question/30599101
#SPJ11
Write an equation in the form y = m x + b for the following table:
x y
-6 -42
-4 -26
-2 -10
0 6
2 22
4 38
6 54
8 70
y= ?
Answer: y=8x+6
Step-by-step explanation:
The slope is
\(\frac{70-54}{8-6}=\frac{16}{2}=8\)
So, the slope is 8.
Since the y-intercept is 6, the equation is y=8x+6.
(T/F) the central limit theorem guarantees an approximately normal sampling distribution when n is sufficiently large.
The given statement "the central limit theorem guarantees an approximately normal sampling distribution when n is sufficiently large." is true because the sampling distribution of the means will approach a normal distribution as the sample size increases.
The Central Limit Theorem (CLT) is a fundamental theorem in statistics that describes the behavior of the means of a large number of independent and identically distributed (iid) random variables.
As a general rule of thumb, a sample size of 30 or greater is often considered "sufficiently large" for the CLT to apply, although this may vary depending on the specific application.
So, to answer the question, we can say that the statement "the central limit theorem guarantees an approximately normal sampling distribution when n is sufficiently large" is true.
However, it is important to note that the CLT only guarantees an approximate normality of the sampling distribution, not an exact normality.
To know more about central limit theorem here.
https://brainly.com/question/18403552
#SPJ4
10.04 × 8.8= ?
can you help me again please
Answer:
10.04 × 8.8 =?, ? = 88.352 :)
Answer:
88.352
Step-by-step explanation:
10.04
x. 8.8
=88.352
Ray NP is angle bisector of angle MNQ and measure of angle PNQ= 2x+1. find measure of angle MNQ
C.
An angle bisector splits angles into halves thus resulting in PNQ. The total angle is however twice the PNQ so 4x + 2.
Hope this helps.
You start a lawn mowing service. You pay $75 for the lawn mower and plan on charging $25 per lawn. Write an equation to relate your income y to the number of lawns you mow x.
Answer:
y = 25x - 75
Step-by-step explanation:
Evaluate Sigma 5 n=1 3(-2)^n-1
Answer choices
-93
-33
33
93
Answer:
93
Step-by-step explanation:
the answer is 93 no -93 i think so
Scott has a blueprint of the new deck he is building with dimensions 7.5 inches by 4.5 inches. the actual deck will have dimensions 20 feet by 12 feet. what is the scale?
The scale factor of the blueprint of the deck is 1.5 inches = 4 feet
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, Scott has a blueprint of the new deck he is building with dimensions 7.5 inches by 4.5 inches. The actual deck will have dimensions 20 feet by 12 feet.
We need to find the scale factor,
7.5 / 20 = 1.5 / 4
Therefore,
There are 1.5 inches in 4 feet
Hence, the scale factor of the blueprint of the deck is 1.5 inches = 4 feet
Learn more about scale factors, click:
https://brainly.com/question/30215119
Answer:
hi
Step-by-step explanation:
guvuvugjdhddiebeidgddb
Which of the following does NOT describe the relationship between any function,
f (x), and its corresponding inverse function f-1 (x)?
A. The graph of f(x) and f-1(x) are symmetrical about the line y=x.
B. The domain and range of the function, f(x), are reversed in the inverse of the function, f-1(x).
C. The inverse of a function, f-1(x), contains all the same points as the original function, f(x).
D. The inverse of a function, f-1(x), is not always a function itself.
Using the concept of inverse function, it is found that the correct option, that is, the false statement is given by:
C. The inverse of a function, f-1(x), contains all the same points as the original function, f(x).
-----------------
An inverse relationship, that is, an inverse function, is a relationship that maps point (x,y) to point (y,x), that is, point (x,y) in the original function is point (y,x) in the inverse function, which means that the inverse function does not contain all the same points as the original, and option c is the answer to this question.The graph of the function and it's inverse are symmetric about the line y = x, thus option a is correct.In the inverse function, the domain and range are reversed from the original, thus statement b is correct.The inverse is only a function if on the original function one value of the output corresponds to one value of the input, that is, \(f(a) = f(b)\) if, and only if, \(a = b\), thus statement d is correct.A similar problem is given at https://brainly.com/question/23950969
an insurance representative has appointments with four prospective clients. from past experience, she knows the probability of making a sale on any appointment is 0.20. what is the probability that she will sell a policy to three of the four prospective clients? what is the probabilty she sells to more than two?
The probability that the insurance representative will sell a policy to three out of four prospective clients is 0.0256.
The probability that the insurance representative sells to more than two prospective clients is 0.0272.
To calculate the probability that the insurance representative will sell a policy to a specific number of prospective clients out of four, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = \((n C k) * p^k * (1 - p)^(n - k)\)
Where:
P(X = k) is the probability of exactly k successes (selling a policy) out of n trials (appointments).
(n C k) represents the combination or "n choose k" which calculates the number of ways to choose k successes out of n trials.
p is the probability of success on a single trial (probability of making a sale).
(1 - p) is the probability of failure on a single trial (probability of not making a sale).
Using this formula, we can calculate the probability of selling a policy to three out of four prospective clients.
Probability of selling a policy to three clients:
P(X = 3) = (4 C 3) * (0.20)^3 * (1 - 0.20)^(4 - 3)
Calculating:
P(X = 3) = 4 * 0.008 * 0.80
P(X = 3) = 0.0256
To calculate the probability that she sells to more than two clients, we need to sum the probabilities of selling to three clients and selling to all four clients.
Probability of selling to more than two clients:
P(X > 2) = P(X = 3) + P(X = 4)
Substituting the values:
P(X > 2) = \(0.0256 + (4 C 4) * (0.20)^4 * (1 - 0.20)^(4 - 4)\)
Calculating:
P(X > 2) = 0.0256 + 1 × 0.0016 × 1
P(X > 2) = 0.0272
Learn more about Probabaility here:
https://brainly.com/question/31828911
#SPJ11
can someone please explain how to find the quotient of 405/27 fraction using long division? :)
The quotient of 405/27 fraction using division is 15.
How to calculate the fraction?It should be noted that the information is simply to divide the numbers.
In this case, the numerator is 405 and the denominator is 27
Therefore, the quotient based on the information illustrated will be:
= 405 / 27
= 15
Therefore, the quotient is 15.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Kyra went to the grocery store on Monday and bought 5 apples and 2 oranges for a total of $3.45. On Thursday she bought 3 oranges and 7 apples for a total of $4.90. What is the cost of apples and oranges?
Answer:
Apple = $0.55
Orange = $0.35
Step-by-step explanation:
Let A = cost of an apple
Let R = cost of an orange
Monday: 5A + 2R = 3.45
Thursday: 3R + 7A = 4.90
Rewrite 5A + 2R = 3.45 to make R the subject:
⇒ 2R = 3.45 - 5A
⇒ R = 1.725 - 2.5A
Substitute R = 1.725 - 2.5A into 3R + 7A = 4.90 and solve for A:
⇒ 3(1.725 - 2.5A) + 7A = 4.90
⇒ 5.175 - 0.5A = 4.90
⇒ 0.5A = 0.275
⇒ A = 0.55
Substitute found value for A into 5A + 2R = 3.45 and solve for R:
⇒ 5(0.55) + 2R = 3.45
⇒ 2.75 + 2R = 3.45
⇒ 2R = 0.7
⇒ R = 0.35
Answer:
apples cost $0.55 each, orange costs $0.35 each
Step-by-step explanation:
let apples be a, let the oranges be o
make equations:
5a + 2o = $3.45 ............equation 13o + 7a = $4.90 ............equation 2
make a the subject for equation 1:
\(\sf 5a + 2o = $3.45\)
\(\sf 5a = 3.45 - 2o\)
\(\sf a = \frac{3.45 - 2o}{5}\)
solve:
\(3o + 7(\sf \frac{3.45 - 2o}{5}) = $4.90\)
\(\sf 0.2o+4.83=4.9\)
\(\sf o=0.35\)
each orange cost $0.35
For apples:
\(\sf a = \frac{3.45 - 2o}{5}\)
\(\sf a = \frac{3.45 - 2(0.35)}{5}\)
\(a=0.55\)
each apples cost $0.55