Let W1 and W2 be independent random exponential random variables with different parameters: W1∼Exp(λ1), independent of W2∼Exp(λ2). (a) Find the pdf for W=min{W1,W2}. (b) Find E(W2∣W1>0.6601). (c) Find E(W1∣W1>0.6601). (d) Find P(W2>1). (e) Find P(W2>W1). (f) Find E(W2∣W2>W1)). (g) Find E(W1∣W2>W1)).
Answers
(a) The probability density function for W=min{W1, W2} is fW(w) = (λ1+λ2) * e^(-(λ1+λ2)w).
(b) E(W2 | W1 > 0.6601) = 1/λ2.
(c) E(W1 | W1 > 0.6601) = 1/λ1.
(d) P(W2 > 1) = e^(-λ2).
(e) P(W2 > W1) = 1/2.
(f) E(W2 | W2 > W1) = 1/λ2.
(g) E(W1 | W2 > W1) = 1/λ1.
(a) To find the probability density function (pdf) for W=min{W1, W2}, we can consider the complementary event: P(W > w) = P(W1 > w, W2 > w). Since W1 and W2 are independent, we can multiply their probabilities:
P(W > w) = P(W1 > w) * P(W2 > w) = e^(-λ1w) * e^(-λ2w) = e^(-(λ1+λ2)w).
Now, we can differentiate with respect to w to obtain the pdf:
fW(w) = d/dw [P(W > w)] = d/dw [e^(-(λ1+λ2)w)] = (λ1+λ2) * e^(-(λ1+λ2)w).
(b) E(W2 | W1 > 0.6601):
Since W1 and W2 are independent, their conditional expectation is equal to their expectation. Hence, E(W2 | W1 > 0.6601) = E(W2) = 1/λ2.
(c) E(W1 | W1 > 0.6601):
Similarly, since W1 is exponential, its conditional expectation is given by E(W1 | W1 > 0.6601) = 1/λ1.
(d) P(W2 > 1): P(W2 > 1) = 1 - P(W2 ≤ 1) = 1 - (1 - e^(-λ2*1)) = e^(-λ2).
(e) P(W2 > W1):
To find this probability, we need to consider the joint distribution of W1 and W2. However, it can be observed that W2 > W1 only if W1 > W2. Since W1 and W2 are independent exponential random variables, P(W1 > W2) = 1/2.
(f) E(W2 | W2 > W1):
Similarly to part (b), since W1 and W2 are independent, their conditional expectation is equal to their expectation. Thus, E(W2 | W2 > W1) = E(W2) = 1/λ2.
(g) E(W1 | W2 > W1):
Again, using the property that W1 and W2 are independent, their conditional expectation is equal to their expectation. Therefore, E(W1 | W2 > W1) = E(W1) = 1/λ1.
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Related Questions
Problem 1. The steady-state response of a damped, linear system to a sinusoidal input U sin(ωt) takes the form xss(t) = X sin(ωt + φ)
If φ < 0, the output is said to "lag" the input whereas, if φ > 0, the output is said to lead the input. Consider the following first order LTI ODE with forcing:
˙x + 5x = 2sin(10t)
What is the steady-state amplitude X and the steady-state phase φ? Plot input versus time and output versus time on the same plot. (You may use a computer if you prefer, but a neat hand-sketch is acceptable.) Does the steady-state response xss(t) lead or lag the input?
Answers
The steady-state amplitude is X = 2/√(29) and the steady-state phase is φ = -tan^(-1)(10/√29), the steady-state response xss(t) lags the input.
The steady-state response of the given system is a sinusoidal function with amplitude X and phase φ. Using the formula for steady-state response, we can find the values of X and φ for the given system. The output is said to lag the input if the phase is negative, which is the case here. We can plot the input and output versus time on the same graph to visualize the lag.
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Express the formula d=rt in terms of the time,t. Use your formula to find the time when the distance is 40 and the rate is 8.
Answers
The expression for d=rt in terms of the time is t = d/r; t = 5.
What is time? Time can be defined as a continuous and ongoing sequence of events that occur consecutively from the past to the present to the future. Time is used to measure, measure or compare the duration of events or the intervals between them, and even the sequence of events. Time is a useful concept that we use in our daily life. We have to watch when we cook, play, study, go to school, meet someone, etc. So knowing the right time is very important. Time is usually the answer to when an event happens or happened. The concept of time determines when a certain event occurs, has occurred or will occur. Time is a measurable quantity and is also infinite. The time is calculated in seconds, minutes, hours, days, months and years.Therefore,
In the equation d=rt
t = d/r
when distance is 40 and the rate is 8
t = d/r
Replace d with 40 and rate with 8
t = 40/8
t = 5
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how do you apply your knowledge about correlation and causation to real life?
PLEASE ANSWER ASAP!!! WILL GIVE BRANLIEST TO FIRST AND MOST CORRECT ANSWER!!!
and please answer this too!!
CONSTRUCT A BOX PLOT WITH THIS GIVEN INFORMATION
NUMBER OF STUDENTS
45 43
34 38
21 36
41 39
23 40
27 23
56 29
33 56
29 44
37 33
ALL THE NUMBERS ABOVE MUST BE IN ONE BOX PLOT!!!!
THANK YOU!!!
PLEASE ANSWER THE BOTH QUESTIONS ASAP!!!
Answers
Answer:
Both positive correlations and negative correlations (when one variable increases as the other decreases) can be found everywhere you look. For example, when you spend more time in sunlight, your chances of getting a sunburn also go up. More examples of positive correlations include:
The more time you spend running on a treadmill, the more calories you will burn.
The longer your hair grows, the more shampoo you will need.
Step-by-step explanation:
21,23,23,27,29,29,33,33,34,36,37,38,39,40,41,43,44,45,56,56
The minimum is the lowest number in the data set. Since it is listed from smallest to largest, we know that the minimum is 21. The median is the middle number. Cancel out 9 numbers from each side and add the two numbers 36+37 then divide the answer by 2 to get the median.Therefore, the median is 36.5
The maximum is the highest number in the data set; it is 56.
Please answer:
p - 4 = -9 + p
Answers
Answer:
There are no values of p that make the equation true.
(No solution)
Step-by-step explanation:
Answer:
\(\mathrm{No\:Solution}\)
Step-by-step explanation:
\(p-4=-9+p\)
Step 1: Subtract \(p\) from both sides
\(p-4-p=-9+p-p\\\\-4=-9\)
Since negative four is not equal, and does not equal negative 9, the answer is \(\mathrm{No\:Solution}\), NOT that there is NO SOLUTION.
Which is the correct classification of startroot 18 endroot? irrational number, non-repeating decimalirrational number, terminating decimalrational number, terminating decimalrational number, non-repeating decimal.
Answers
The correct classification is startroot 18 enroot is (B) a non-repeating decimal irrational number.
What is a non-repeating decimal irrational number?A decimal number that never ends and never repeats itself is known as a non-terminating, non-repeating decimal. Such decimals are irrational numbers since they cannot be expressed as fractions. Pi is a decimal that doesn't end or repeat.Non-recurring numbers in mathematics are those whose values don't repeat themselves after a decimal point. Non-terminating decimals and non-Repeating Decimal Numbers are other names for them. As an illustration, √2 = 1.41421356237309504.So, we have: startroot 18 endroot
Which is,
√18
√2 × 9
3√2
This number has non-repeating decimals and is irrational.
Therefore, the correct classification is startroot 18 enroot is (B) a non-repeating decimal irrational number.
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Correct question:
Which is the correct classification of startroot 18 endroot?
a. irrational number,
b. non-repeating decimal irrational number,
c. terminating decimalrational number,
d. terminating decimalrational number,
e. non-repeating decimal.
solve for x.28+19x=-8+15x
Answers
28+19x=-8+15x
Move the variable terms ( the one with "x" ) to the left side of the equation.
19x-15x = -8-28
4 x = -36
Divide both sides by 4:
4x/4 = -36/4
x= -9
A shipping service charges $0.41 for the first ounce and $0.21 for each additional ounce of package weight, Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1.
Answers
We know that they charge $0.41 for the first ounce and $0.21 for each additional ounce.
Based on the given information, we can define the following equation
\(P=0.41+0.21x\)Where x represents ounces.
plz help answer fast
Answers
Answer:
d because it does not looks somlar
Answer:
d
Step-by-step explanation:
one angLe is common
2/4 != 3/4.5 !=3/5
not similar
Which simplified expression matches the perimeter of the shape?
Answers
hope it helps
tosha has 8 coins in her pocket. she has a mixture of pennies, nickels, dimes and quarters, but she has no more than 3 of any coin. what is the largest amount of money she could possibly have?
Answers
The largest amount of money she could have is: (3 x 25 cents) + (3 x 10 cents) + (2 x 5 cents) = 75 cents + 30 cents + 10 cents = 115 cents or $1.15.
To find the largest amount of money Tasha could have with 8 coins in her pocket, we need to consider the different combinations of coins she could have. Since she has no more than 3 of any coin, the possibilities are:
- 3 quarters, 2 dimes, 1 nickel, 2 pennies = $0.81
- 3 quarters, 2 dimes, 2 nickels, 1 penny = $0.80
- 3 quarters, 2 nickels, 3 pennies = $0.78
- 3 quarters, 1 dime, 3 nickels, 1 penny = $0.76
- 3 quarters, 1 dime, 2 nickels, 3 pennies = $0.74
- 3 quarters, 1 dime, 1 nickel, 4 pennies = $0.73
- 2 quarters, 3 dimes, 1 nickel, 2 pennies = $0.70
- 2 quarters, 3 dimes, 2 nickels, 1 penny = $0.69
- 2 quarters, 2 dimes, 3 nickels, 1 penny = $0.68
- 2 quarters, 2 dimes, 2 nickels, 2 pennies = $0.67
Therefore, the largest amount of money Tasha could have is $0.81 with 3 quarters, 2 dimes, 1 nickel, and 2 pennies.
To maximize the amount of money Tosha could have with 8 coins and no more than 3 of any coin, she should carry the coins with the highest denominations. In this case, she can have 3 quarters (25 cents each), 3 dimes (10 cents each), and 2 nickels (5 cents each). The largest amount of money she could have is:
(3 x 25 cents) + (3 x 10 cents) + (2 x 5 cents) = 75 cents + 30 cents + 10 cents = 115 cents or $1.15.
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#1 BRAINLIST
SHow all steps pls it was due yesterday!
Answers
Answer:
Step-by-step explanation:
1.Since product owners support a continuous pipeline that fully automates deployments with no manual conformity step, stories that are cleared for automatic ...
Answers
Product owners play a crucial role in supporting a continuous pipeline that enables automated deployments without the need for manual conformity steps. This ensures that stories that meet the necessary criteria can be automatically cleared for deployment.
In modern software development practices, a continuous pipeline is often employed to streamline the process of delivering software updates. This pipeline includes various stages such as development, testing, and deployment. Product owners, as key stakeholders in the development process, contribute to the successful implementation of this pipeline.
By supporting a continuous pipeline, product owners enable the automation of deployments, eliminating the need for manual conformity steps. This means that once a story or feature has been developed and tested, it can be automatically cleared for deployment if it meets the necessary criteria. This automation significantly speeds up the release process, reduces the potential for human error, and allows for faster feedback and iteration cycles.
Product owners collaborate closely with the development team and stakeholders to define the criteria that determine when a story is ready for automatic deployment. These criteria may include passing all relevant tests, meeting user acceptance criteria, and fulfilling any necessary compliance or security requirements. By ensuring that these criteria are clearly defined and communicated, product owners help maintain the quality and reliability of the software being delivered.
In conclusion, product owners play a critical role in supporting a continuous pipeline that enables automated deployments without the need for manual conformity steps. Their involvement ensures that stories meeting the necessary criteria can be seamlessly cleared for deployment, promoting efficiency, reliability, and faster delivery of software updates.
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how do you do this? please answer!
Answers
Answer:
k = 3, q = 9
Step-by-step explanation:
hmm.... what k will end up giving that 6x on the right side of the equation?
Since 6x is the second thingy in that expression, its a good idea to try dividing by 2, lets try k = 6/2 = 3!
(x+3)^2 = x^2+3x+3x+9
(x+3)^2 = x^2+6x+9
that fits pretty good!
So, k = 3, q = 9
-SC
a girl is about to enter puberty. how long will the total process take? group of answer choices about 5 years, for every child about 2 years, for every child about 9 years, for every child a variable length of time for different girls
Answers
The total duration of the puberty process can be different for each girl who is about to enter it, as the length of time for the different stages of puberty can vary from person to person. Hence, if a girl is about to enter puberty, the total process will take a variable length of time for different girls.
The total process of puberty for a girl can take a variable length of time, but typically it takes around 2 to 5 years to complete. The onset of puberty usually occurs between the ages of 8 and 13, with most girls starting around age 11.
The process of puberty includes physical changes such as breast development, the growth of pubic and underarm hair, and the onset of menstruation.
The duration of puberty can also depend on factors such as genetics, nutrition, and overall health. Some girls may experience a shorter or longer duration of puberty than others. However, in general, the process of puberty for a girl usually takes around 2 to 5 years to complete.
Therefore, the correct answer is "a variable length of time for different girls", but typically takes around 2 to 5 years to complete.
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|x|+4=-9 solve for absolute value
Answers
Answer:
no solution
Step-by-step explanation:
|x|+4=-9
Solving an absolute value equation
Subtract 4 from each side
|x|+4-4=-9-4
|x|=-13
Since |x| must be non-negative, there is no solution
Consider trapezoid KLMN
. Trapezoid KLMN
is reflected across the x
- and y
-axes to form trapezoid K′L′M′N′.
What is the length of line segment K′N′
?
Responses
3
units
3 units
6
units
6 units
9
units
9 units
12
units
Answers
The required length for line segment K'N' is 9 units. So correct option is C.
Describe trapezoid?A trapezoid is a two-dimensional geometric shape that is defined as a quadrilateral with one pair of parallel sides. It is also known as a trapezium in some countries. The other two sides of a trapezoid are typically non-parallel and can be of different lengths.
Trapezoids can be classified into two types: isosceles trapezoids and non-isosceles trapezoids. Isosceles trapezoids have equal lengths of the non-parallel sides, while non-isosceles trapezoids have unequal lengths.
The area of a trapezoid can be calculated using the formula: (base1 + base2) x height / 2, where base1 and base2 are the lengths of the parallel sides, and height is the perpendicular distance between the parallel sides.
The perimeter of a trapezoid can be calculated by adding the lengths of all four sides together. If the trapezoid is isosceles, the perimeter can be calculated using the formula: 2 x (side length) + (sum of the lengths of the parallel sides).
Trapezoids can also be used to solve problems in real-world situations, such as calculating the area of a trapezoidal roof or finding the distance between two parallel lines. They are also commonly used in geometry problems and proofs.
In summary, a trapezoid is a quadrilateral with one pair of parallel sides. It can be classified as isosceles or non-isosceles and can be used to calculate area and perimeter, as well as solve problems in geometry and real-world situations.
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Sanjana wants to buy a computer that she can use for school next year which is 9 months away. She discovers that she can buy a computer for $400 at a discount electronics store in town. How much does Sanjana have to save every MONTH to buy the computer? ANSWER: $400 / 9 months = $44.44/mo How much does Sanjana have to save every WEEK to buy the computer? ANSWER: $44.44 / 4 weeks = $11.11/wk How much does Sanjana have to save every DAY to buy the computer? ANSWER: $11.11 / 7 days = $1.59/day
Answers
Answer: ANSWER: $400 / 9 months = $44.44/mo How much does Sanjana have to save every WEEK to buy the computer? ANSWER: $44.44 / 4 weeks = $11.11/wk How much does Sanjana have to save every DAY to buy the computer? ANSWER: $11.11 / 7 days = $1.59/day
Step-by-step explanation:
Find the two values that x can have if 5x ^ 2 + 41 = 86
Answers
Answer:
x= 3 or x = -3
Step-by-step explanation:
We can see here that the two values that x can have if 5x² + 41 = 86 is -3 and +3.
How we arrived at the solution?To find the values of x that satisfy the equation 5x² + 41 = 86, we can start by isolating the term with the variable on one side of the equation. Here's the step-by-step solution:
Subtract 41 from both sides of the equation:
5x² + 41 - 41 = 86 - 41
5x² = 45
Divide both sides of the equation by 5:
(5x²) / 5 = 45 / 5
x² = 9
Take the square root of both sides of the equation:
√(x²) = √9
x = ±3
Therefore, the equation 5x² + 41 = 86 has two solutions: x = 3 and x = -3.
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I need help pleaseee
Answers
9514 1404 393
Answer:
297 miles
Step-by-step explanation:
The round-trip distance from X to Y is double the one-way distance. The distance from X to Y is 648/2 = 324 miles.
That distance is the sum of distances from X to Z and Z to Y. Then ...
XZ +ZY = XY
27 +ZY = 324
ZY = 297
It is 297 miles from City Z to City Y.
Identify the features of cross-tabulation. (Check all that apply.)
-It is easy to create an endless variety of cross-tabulation tables.
-It gives research analysts a strong tool to summarize survey data.
Answers
The features of cross-tabulation include its versatility in creating a wide range of tables and its effectiveness as a tool for summarizing survey data.
Cross-tabulation, also known as contingency table analysis or crosstab, is a statistical technique used to analyze the relationship between two or more categorical variables.
It involves organizing data into a table format to display the frequency distribution of variables across different categories.
One feature of cross-tabulation is that it allows for the creation of a variety of tables based on the specific research question or objective.
Researchers can choose different variables to cross-tabulate and arrange the categories in various ways, providing flexibility in examining relationships and patterns within the data.
This versatility allows for the exploration of different hypotheses and the identification of significant associations between variables.
Another feature of cross-tabulation is its effectiveness as a tool for summarizing survey data.
By organizing data into a table format, cross-tabulation provides a clear and concise summary of the relationships between variables.
It allows research analysts to compare the frequencies and proportions of different categories across variables, making it easier to identify patterns, trends, and associations within the data.
This summary information is valuable for gaining insights, drawing conclusions, and making informed decisions based on the survey results.
In conclusion, cross-tabulation offers the advantages of versatility in creating a wide range of tables and providing research analysts with a powerful tool to summarize survey data effectively.
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PLEASE HELP ME ON THIS ONE
Answers
Answer:
8m
Step-by-step explanation:
Find the volume of the sphere first :
V sphere = \(\frac{4}{3}\) π 6^3 = 902.51
Then use the volume of the sphere to find the height :
Formula = V/π\(r^{2}\)
902.51/π(6)^2 = 8.004 (rounded is 8)
hope this helped :)
Answer:
8 m
Step-by-step explanation:
Given,
Volume of sphere = Volume of cylinder
Radius ( r ) = 6 m
Formula : -
Volume of sphere = 4/3 πr³
Note : -
The value of π is 3.14
Volume of sphere
= 4/3 x 3.14 x 6³
= 4/3 x 3.14 x 6 x 6 x 6
= 904.32 m³
Hence,
The volume of sphere is 904.32 m³.
Since,
Volume of sphere = Volume of cylinder
So,
Volume of cylinder = 904.32 m³
Formula : -
Volume of cylinder = πr²h
πr²h = 904.32
3.14 x 6 x 6 x h = 904.32
113.04 x h = 904.32
Divide 113.04 on both sides,
h = 904.32 / 113.04
h = 8 m
help me for brainitest pls
Answers
Answer:
3/6+4/6=7/6 (or 1 1/6)
Step-by-step explanation:
Multiply 1/2 by 3, add the top and bottom numbers together
Then I simplified 7/6 to 1 1/6 because 7 goes into 6, 1 time and there is still 1 remaining
Help me please!!!! Anybody.thanks
Answers
Answer:
Hey avagharrison !
• Question a)
\( { \tt{ \frac{29 \times 31}{0.27} }} \\ \\ \dashrightarrow \: { \boxed{ \tt{3330 \: \: [1 \: s.f]}}}\)
• Question b)
\({ \tt{ \frac{4.8 \times 37}{0.21} }} \\ \\ \dashrightarrow \: { \boxed{ \tt{846 \: \: [1 \: s.f]}}}\)
• Question c)
\({ \tt{ \frac{9.7 \times 26}{0.022} }} \\ \\ \dashrightarrow \: { \boxed{ \tt{11464 \: \: [1 \: s.f]}}}\)
s.f stands for significant figure.
please answer!! it’s 12:08 am and i’m trying to get these two questions done
Answers
Answer:
21 and 14
Step-by-step explanation:
The relationship between x and y is proportional thus the equation is
y = kx ← k is the constant of proportion
To find k use the ordered pair y = 84 when x = 28 , then
84 = 28k ( divide both sides by 28 )
k = 3
y = 3x ← equation of proportion
When x = 7 , then
y = 3 × 7 = 21 ← value required in top table
When y = 42 , then
42 = 3x ( divide both sides by 3 )
x = 14 ← value required in lower table
Jenna feeds her cat twice a day. She gives her cat 3/4 can of cat food each time. Jenna is having a friend take care of her cat for 5 days. To prepare, she bought 8 cans of cat food, did Jenna buy enough cat food?
Answers
Answer:
Number of times Jenna feeds her cat = 2
Cat food each time
Number of days = 5
Number of cans she bought = 8
Step-by-step explanation:
Required food for each time
Jenna feeds her cat twice a day
Required food for a day
Required food for 5 days
Since, 7.5 cans < 8 cans, therefore, Jenna did buy enough cat food for her cat.
Nina sells 24 of her 52 CDs. Write the fraction of the CDs that Nina sells in simplest form.
Answers
Answer:
6/13
Step-by-step explanation:
if u use the highest common factor 4,U get 6 when u divide 24 by 4 and 13 when you divide 52 by 4.
I hope this helps in any way :)
PLEASE HELP
Rock it out builds stage sets for rock concerts in the shape of a square pyramid. One set has a base that is 12 feet long and 12 feet wide. The slant height of the set is 13 feet. What is the surface area of the stage set?
Answers
Answer:
I am pretty sure it's 312ft^2
Step-by-step explanation:
If you do 12x13/2 its 78
then you would do 78 x 4
and you get 312
so its 312ft^2
Heeeeellllllllllllpppppppppp
Answers
As the test statistic becomes larger, the p-value a. gets smaller b. becomes larger c. stays the same, since the sample size has not been changed
Answers
as the test statistic becomes larger, the p-value gets smaller, indicating stronger evidence against the null hypothesis.
The p-value is a measure of the strength of evidence against the null hypothesis in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme as or more extreme than the one obtained, assuming the null hypothesis is true.
In general, a larger test statistic indicates stronger evidence against the null hypothesis, suggesting that the observed data deviates more from what would be expected under the null hypothesis. As a result, the p-value associated with a larger test statistic becomes smaller.
The p-value is calculated based on the test statistic and the null distribution, which represents the distribution of the test statistic under the assumption that the null hypothesis is true. A larger test statistic corresponds to a point further into the tails of the null distribution, where the probability density is lower. Hence, the p-value, which represents the tail probability beyond the observed test statistic, decreases as the test statistic becomes larger.
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A company makes cell phones in two different factories, one abroad and one more local. At the factory abroad it takes 30 hours to produce the cellphone and at the local factory it takes 20 hours. The costs of producing these cell phones are $20 each at the factory abroad and $60 each at the local factory. The company's total labor force can provide 6000 hours of labor each week and total resources are $12,000 each week. How many cell phones should the company make at each factory to maximize the amount of phones produced?
Answers
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of phones produced abroad and y represent the number of phones produced locally.
The company can provide 6000 hours of labor each week and it takes 30 hours to produce the cellphone abroad and at the local factory it takes 20 hours, hence:
30x + 20y = 6000 (1)
Also, there is a total resource of $12000 each week, the cost of producing abroad is $20 and the cost of producing locally is $60. Hence:
20x + 60y = 12000 (2)
Multiply equation 1 by 3 and subtract equation 2 from the result. This gives:
70x = 6000
x = 600/7 ≈ 86
Put x = 86 in equation 1:
30(86) + 20 y = 6000
20y = 3420
y = 171
86 phones should be produced abroad and 171 phones locally