Use the simplex method to solve the linear programming problem Maximize z=7X1 + 5x2 + x3 subject to 5x1 +5x2 + x3 = 25 x1 + 3x2 + 5x3 = 13 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0
Select the correct choice below and if necessary, fill in the answer boxes to complete your choice A. The maximum is when x1= x2= s1= and s2=
B. There is no maximum
Answers
The value will be maximum when x1 = 3, x2 = 2, s1 = 0, and s2 = 0.
To solve the linear programming problem using the simplex method, we need to convert the problem into standard form by introducing slack variables. The standard form of the given problem becomes:
Maximize z = 7x1 + 5x2 + x3
subject to
5x1 + 5x2 + x3 + s1 = 25
x1 + 3x2 + 5x3 + s2 = 13
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, s1 ≥ 0, s2 ≥ 0
The initial tableau for the simplex method is:
| Cb | x1 | x2 | x3 | s1 | s2 | RHS |
|----|----|----|----|----|----|-----|
| 0 | -7 | -5 | -1 | 0 | 0 | 0 |
| s1 | 5 | 5 | 1 | 1 | 0 | 25 |
| s2 | 1 | 3 | 5 | 0 | 1 | 13 |
Performing the simplex iterations, we find:
Iteration 1:
Pivot Column: x1 (most negative coefficient in the objective row)
Pivot Row: s1 (minimum ratio in the right-hand side column)
Pivot Element: 5 (intersection of pivot column and pivot row)
| Cb | x1 | x2 | x3 | s1 | s2 | RHS |
|---- |----|----|----|----|----|-----|
| s1 | 1 | 1 | 0 | 1 | 0 | 5 |
| x2 | 0 |2 | 1 | -1 | 0 | 20 |
| s2 | 0 | 2 | 5 | 1 | 1 | 8 |
Iteration 2:
Pivot Column: x2 (most negative coefficient in the objective row)
Pivot Row: s2 (minimum ratio in the right-hand side column)
Pivot Element: 2/5 (intersection of pivot column and pivot row)
| Cb | x1 | x2 | x3 | s1 | s2 | RHS |
|----|----|----|----|----|----|-----|
| s1 | 1 | 0 | -1/5 | 3/5 | -2/5 | 1 |
| x2 | 0 | 1 | 2/5 | -1/5 | 2/5 | 4 |
| s2 | 0 | 0 | 17/5 | 3/5 | 1/5 | 4 |
All coefficients in the objective row are non-negative, indicating that the optimal solution has been reached. The maximum value of z is 4, and the corresponding values for x1, x2, s1, and s2 are 3, 2, 0, and 0, respectively.
Therefore, the maximum is when x1 = 3, x2 = 2, s1 = 0, and s2 = 0.
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Related Questions
Answer:
2. Tommy's mom asked him to help her clean the house. His mom has asked him
to sweep his bedroom floor, the laundry room, and the kitchen. He estimates
that it is going to take him 10 minutes to sweep out each room. About how
many minutes will it take Tommy to help his mom
Answers
Answer:
it will take Tommy 30 minutes
Answer:
It'll take him 30 minutes.
Step-by-step explanation:
He estimates that it'll take 10 minutes for each room. His mom asked him to sweep 3 rooms. If you take 10 and multiply it by 3, you get 30.
In a food chain, tertiary consumers are _____ primary producers. Group of answer choices one level above three levels above two levels above one level below
Answers
Tertiary consumers are one level above primary producers in a food chain. In a food chain, the transfer of energy and nutrients occurs from one trophic level to another.
The trophic levels are categorized into producers, primary consumers, secondary consumers, and tertiary consumers.
Primary producers, such as plants or algae, are the first trophic level in a food chain. They convert energy from sunlight into organic matter through photosynthesis. Primary consumers, also known as herbivores, are the organisms that feed directly on primary producers.
Secondary consumers are the next trophic level and they feed on primary consumers. They are usually carnivores or omnivores that consume herbivores.
Finally, tertiary consumers occupy the highest trophic level in a food chain. They are the top predators that feed on secondary consumers. These can include large carnivores or even apex predators.
Therefore, tertiary consumers are one level above primary producers in the food chain. They represent the organisms that obtain energy by consuming other organisms higher up in the trophic hierarchy.
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g(n)=-3n-4; Find g(-8)
Answers
Answer:
g(- 8) = 20
Step-by-step explanation:
substitute x = - 8 into g(x) , that is
g(- 8) = - 3(- 8) - 4 = 24 - 4 = 20
Help me please, I really don't want to fail
Which system of equations has no solution?
Answers
Answer: Top left i'm pretty sure
Step-by-step explanation: Because there isn't a blue line and you need a blue line for it to be an equation
Answer:
Parallel line
Step-by-step explanation:
The parallel line doesn't connect so it a infinite therefore it means its a no solution line
help me pls thx
It costs $20 to buy 5 sandwiches from a vending machine. At this rate, what is the cost for 8 sandwiches? If you get stuck, consider creating a table.
Answers
Answer:
$ 32
Step-by-step explanation:
20 ÷ 5 = 4
Four dollars per sandwich
4 x 3 = 12
20 + 12 = 32
or
8 x 4 = 32
Perform the indicated operation.
(-6) (4)
Answers
Answer:
If your multiplying and the equation is -6 x 4 then your answers gonna be -24
Step-by-step explanation:
But if its something else, sorry, I can't hep you unless I get a further explanation.
Answer:
-24
Step-by-step explanation:
(-6)×(4)
-24
invisible plus at the front of four
-×+=-
juice: 48 fluid ounces for $2.07; 32 fluid ounces for $1.64
Answers
Answer:
Step-by-step explanation:
Start by changing the dollars into cents.
2.07 dollars = 2.07 * 100 = 207 cents
1.64 dollars = 1.64 * 100 = 164 cents.
How much does 1 ounce cost for each?
207 cents / 48 = 4.3125 cents / oz
164 / 32 = 5.125
The better buy is the 48 fluid oz jar.
determine the domain of the following graph
Answers
Answer:
[-5, 10) or you can write \(-5\le x < 10\)
Step-by-step explanation:
The domain is the set of all values of x used in the function. Scan across the graph from left to right (much as you do when reading). The first point you find on the graph has an x-coordinate 5 (see the solid dot?). Then, as you continue reading across the graph, there are values of x used until you get to 10. The dot at x = 10 is open, not filled in. That indicates that the number x = 10 is NOT used by the function.
So the domain is all real numbers greater than or equal to -5 and less than 10.
[-5, 10) is called interval notation; a square bracket means the value next to it IS used by the function, a parenthesis means the value next to it is NOT used.
Find the area of the triangle.
8 in.
12 in.
in
?
The area of the triangle is
Answers
Answer:
48 in²
Step-by-step explanation:
Hello!
Area of a Triangle: \(A = \frac12 b*h\)
Given that the base and height are 8 and 12, we can plug it into the formula to solve for the area.
Find the area\(A = \frac12 b*h\)\(A = \frac12 (8*12)\)\(A = \frac12 (96)\)\(A = 48\)The area of the triangle is 48 in².
\(\huge\text{Hey there!}\)
\(\huge\textbf{Formula for finding area of triangle:}\)
\(\mathsf{\dfrac{1}{2}\times \bold{b}ase\times \bold{h}eight}\)
\(\huge\textbf{Your equation should look like:}\)
\(\mathsf{\dfrac{1}{2}\times 8 \times 12}\)
\(\huge\textbf{Making it easier to solve:}\)
\(\mathsf{\dfrac{1}{2}\times 8 \times 12}\)
\(\mathsf{= \dfrac{1}{2}\times \dfrac{8}{1} \times \dfrac{12}{1}}\)
\(\mathsf{= \dfrac{1\times8\times 12}{2\times1\times1}}\)
\(\mathsf{= \dfrac{8\times 12}{2\times1}}\)
\(\mathsf{= \dfrac{96}{2}}\)
\(\mathsf{= \dfrac{96\div 2}{2\div 2}}\)
\(\mathsf{= \dfrac{48}{1}}\)
\(\mathsf{= 48\div1}\)
\(\mathsf{= 48}\)
\(\huge\textbf{Therefore, your \boxed{answer} should be:}\)
\(\huge\boxed{\frak{48\ in^2}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
Explain how the quotient of powers property was used to simplify this expression. 2 to the fifth power, over 8 = 22.
Answers
We have been given the expression 2^5/8=2^2 was used to simplify this expression. 2 to the fifth power, over 8 = 22.
8 can be rewritten as 2^3
Hence, the given expression becomes
2^5/2^3=2^2
After subtracting the exponents on left hand side of the equation we get:
2^2=2^2
we can do it by simplifying 8 to 2^3 to make both powers base two, and subtracting the exponents.
Linear expressions or equations are expressions in which the highest power of the variable is one.
Quadratic expressions or equations are expressions in which the highest power of the variable is two.
Cubic expressions or equations are expressions in which the highest power of the variable is three.
Quartic expressions or equations are expressions in which the highest power of the variable is four.
From the expression, 5x + 2 given,
the highest power of x is one. So it is a linear expression.
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The result is 4
A number's exponent indicates how many times the number has been multiplied by itself. Example: Since 2 is multiplied by itself 4 times, 2222 can be expressed as 24. Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base." Generally speaking, xn denotes that x has been multiplied by itself n times.
The quotient of powers property states that if you have an expression in the form (a^m)/(a^n) where 'a' is the base and 'm' and 'n' are integers, it can be simplified to (a^(m-n)).
In the given expression, 2 to the fifth power (2^5) can be divided by 8 (which is equal to 2^3), using the quotient of powers property. The result is 2^(5-3) = 2^2 = 4
So 2^5 / 8 = 4
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which of the following is true regarding the solutions to the logarithmic equation below 2log ^6(x)=2 log ^6 (x^2 )=2 x^2=36 x=6,-6
Answers
Answer:
Step-by-step explanation:
I'm assuming these are logs to the base 6
2 log6 x = 2
log6 x^2 = 2
So x^2 = 6^2
x = 6, -6.
Answer:
It's C
Step-by-step explanation:
Edge 2020!
(e) Elena wants to make sure she bought a total of 5 fruits, one for each school day. What would be the combination she should buy?
(f) Let b be the number of bananas and a be the number of apples. Write the equation that
represents: "the number of bananas and the number of apples must add up to 5”
Answers
Answer:
10 fruit maybe
explanation:CORRECT ME IF I'M WRONG
evaluate the expression when c=2. 6c/2
Answers
Answer:
6Step-by-step explanation:
Given the expression g(c) = 6c/2, we are to find the value when c = 2
Substitute c = 2 into the expression
g(2) = 6(2)/2
g(2) = 12/2
g(2) = 6
Hence the result when c = 2 is 6
Why We Sleep: The New Science of Sleep and Dreams is a popular science book about sleep by the neuroscie
Answers
Answer:
i have no idea what is the question would you please provide me exact questions
Answer:
what?
Step-by-step explanation:
doesnt understand
Solve (x – 3)2 = 49. Select the values of x.
Answers
Answer:
x=27.5 hope it helps you..... and hi
Answer:
Step-by-step explanation:
1....Re-order terms so constants are on the left;
2(x - 3) =49
2.. Distribute;
2x-6 =49
3... Add 6 to both sides;
2x-6+6=49+6
4... Simplify;
2x=55
5..Divide both sides by the same factor;
2x=55
\(\frac{2x}{2}\) = \(\frac{55}{2}\)
6...Simplify;
x=\(\frac{55}{2}\)
The stem-and-leaf plot shows the number of broken crayons in each crayon box at a preschool. What is the greatest number of broken crayons in a box? A 7 crayons B 47 crayons c 477 crayons d 1469 crayons
Answers
Answer:
47
Step-by-step explanation:
Values on a stem and leaf plot can be obtained by using the key :
Stem | leaf
With each value in the stem representing the first digit and the value in the leaf denoting the second digit.
The highest stem value here is 4 and the highest leaf value is 7.
Hence, the highest number of broken crayon is 47.
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be \(w\). It follows that the length is \(w+2\).
\(w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7\)
Prove that there exist prime numbers with arbitrarily many 0's in its digits. (Hint: use Dirichlet's theorem on arithmetic progressions)
Answers
Dirichlet's theorem on arithmetic progressions states that for any two coprime positive integers a and d, there are infinitely many prime numbers of the form a + nd, where n is a non-negative integer. We can use this theorem to prove that there exist prime numbers with arbitrarily many 0's in its digits.
Let's consider the arithmetic progression 10^k, 10^k + 1, 10^k + 2, ..., 10^k + 9. This progression consists of all the positive integers with k+1 digits that end in a non-zero digit. Note that 10^k and 10^k + 1 are coprime, as are 10^k and 10^k + 2, and so on, up to 10^k and 10^k + 9. By Dirichlet's theorem, there are infinitely many primes of the form 10^k + nd, where n is a non-negative integer and d is any one of the 10 numbers 1, 2, ..., 9. Since 10^k has k+1 digits, we can choose k to be any positive integer, and thus there exist prime numbers with arbitrarily many 0's in its digits. For example, if we choose k = 1000, then there exist infinitely many prime numbers with at least 1000 zeros in its digits, since there are infinitely many primes of the form 10^1000 + nd, where d is any one of the 10 digits 1, 2, ..., 9.
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Two students are playing a game. If a player spins a one or a three, he/she gets an extra turn. What is the probability that a player will get an extra turn?
Answers
The probability that a player will get an extra turn is 1/2 or 50%.
There are four possible outcomes when a player spins the spinner: 1, 2, 3, or 4. The probability of spinning a one or a three is 2/4 or 1/2, since there are two favorable outcomes out of four equally likely outcomes.
If a player spins a one or a three, they get an extra turn, which gives them another chance to spin the spinner. Since the probability of spinning a one or a three is 1/2, the probability of getting an extra turn is also 1/2.
Therefore, the probability that a player will get an extra turn is 1/2 or 50%.
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what’s the answer for 15ft wide and 8ft long
Answers
Find the measure of c. A. 10 B. 280 C. 100 D. 140
Answers
Answer:
63°
Step-by-step explanation:
a = 27°
b = 180° - (a + 27°)
b = 180° - (27° + 27°)
b = 180° - 54°
b = 126°
By inscribed angle theorem:
c = 1/2 b = 1/2 * 126°
c = 63°
Solve the following:
4x-1 divided by 2= x+7
a)
b)
3x + 2 = 2x+13 divided by 3
Answers
The equation's answer is x = 7.5. 4x - 1 2 = x + 7.
x = 1 is the answer to the problem 3x + 2 = (2x + 13) 3.
a) To solve the equation 4x - 1 ÷ 2 = x + 7, we need to isolate the variable x. Let's follow the steps:
1: Distribute the division operation to the terms inside the parentheses.
(4x - 1) ÷ 2 = x + 7
2: Divide both sides of the equation by 2 to isolate (4x - 1) on the left side.
(4x - 1) ÷ 2 = x + 7
4x - 1 = 2(x + 7)
3: Distribute 2 to terms inside the parentheses.
4x - 1 = 2x + 14
4: Subtract 2x from both sides of the equation to isolate the x term on one side.
4x - 1 - 2x = 2x + 14 - 2x
2x - 1 = 14
5: Add 1 to both sides of the equation to isolate the x term.
2x - 1 + 1 = 14 + 1
2x = 15
6: Divide both sides of the equation by 2 to solve for x.
(2x) ÷ 2 = 15 ÷ 2
x = 7.5
Therefore, x = 7.5 is the solution to the equation 4x - 1 ÷ 2 = x + 7. However, note that this answer is not an integer, so it may not be valid for certain contexts.
b) To solve the equation 3x + 2 = (2x + 13) ÷ 3, we can follow these steps:
1: Distribute the division operation to the terms inside the parentheses.
3x + 2 = (2x + 13) ÷ 3
2: Multiply both sides of the equation by 3 to remove the division operation.
3(3x + 2) = 3((2x + 13) ÷ 3)
9x + 6 = 2x + 13
3: Subtract 2x from both sides of the equation to isolate the x term.
9x + 6 - 2x = 2x + 13 - 2x
7x + 6 = 13
4: Subtract 6 from both sides of the equation.
7x + 6 - 6 = 13 - 6
7x = 7
5: Divide both sides of the equation by 7 to solve for x.
(7x) ÷ 7 = 7 ÷ 7
x = 1
Hence, x = 1 is the solution to the equation 3x + 2 = (2x + 13) ÷ 3.
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please help, which do I shade green and red?? thanks
Answers
Answer:
shade all of the squares with two capital Ns (NN) red. Shade all the squares with one capital N and one Lowercase n with green. Leave the rest (nn) unshaded.
Step-by-step explanation:
\(shade \: all \: NN \to \boxed {red} \: \to \: \\ (they \: are \: all \: \boxed{ \: dominant \: offsprings} \: ) \\ \\ shade \: all \: Nn \to \boxed {green} \: \to \\ (they \: are \: all \: \boxed{hoterozygous \: }offsprings)\\ \\ shade \: all \: nn \to \: \boxed {nothing} \: \to \\ (they \: are \: all \: \boxed{ \: recessive \:offsprings \: })\)
Please help fast it’s subtraction
Answers
Answer:
17
220
Result in decimals: 0.077272727272727
Step-by-step explanation:
Answer:
\(7\frac{17}{220}\)
Step-by-step explanation:
\(9\frac{8}{11} -2\frac{13}{20}=\\\)
\(9\frac{160}{220} -2\frac{143}{220}=\)
\(=7\frac{17}{220}\)
Hope this helps
Rachel plans to withdraw $5,000 at the end of each year from her bank account that pays 4% interest. How many annual withdrawals can she make if her starting balance is $63,296.48?
Answers
I inferred 4% interest to be per annum.
Answer:
about 19 annual withdrawals
Step-by-step explanation:
First, we note that Rachel plans to withdraw $5,000 at the end of each year from a starting balance is $63,296.48, excluding the 4% interests, the total withdrawals possible is
$63,296.48/$5,000 = 12.65 (in years)
Including the 4% interest;
4% x $63,296.48 = $2,531.85
To find the possible withdrawals we multiply by the initial period excluding interest rates
$2531.85 * 12 = $31,901/5,000= 6.38 (in years)
Total: 6.38 + 12.65 = 19.03 (in years)
5. Which equation below can be transformed into the following equation:
2x + 4 = 6x + 2
2x + ½ = 6x + 1⁄2
2(2x+5)= 4x + x + 2
O2(x+2) = 2 (3x + 1)
Answers
Answer:
The equation that can be transformed into the following equation 2x + 4 = 6x + 2 is:
2(2x+5)= 4x + x + 2
Therefore, the equation 2(2x+5)= 4x + x + 2 can be simplified and transformed to the form of 2x + 4 = 6x + 2.
3) Five times the second of three consecutive odd integers is
thirteen less than three times the sum of the first and third
integers. Find the largest odd integer..
Answers
9514 1404 393
Answer:
15
Step-by-step explanation:
Let x represent the middle odd integer.
5x = 3((x-2)+(x+2)) -13
5x = 6x -13
x = 13 . . . . the middle of 3 consecutive odd integers
The largest odd integer is 15.
Which theorem or postulate proves that △ABC and △DEF are similar? SSS Similarity Theorem AA Similarity Postulate SAS Similarity Theorem Two triangles with the same shape. In the first triangle, the vertices are labeled as A, B, and C. Base is B C and the top vertex is A. Side A B is labeled 3. Side B C is labeled 7. Side A C is labeled 6. In the second triangle, the vertices are labeled as D, E, and F. Base is E F and the top vertex is D. Side D E is labeled 18. Side E F is labeled 42. Side D F is labeled 36
Answers
The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.
In this case, the ratio of the corresponding sides of the two triangles are:
AB/DE = 3/18 = 1/6
BC/EF = 7/42 = 1/6
Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.
O is the center of the regular octagon below. Find its area. Round to the nearest tenth if necessary. 4
Answers
The formula for the area of a regular octagon in proportion to its Apothem, which in this case is 18, is used to arrive at the following result. As a result, the area of the Octagon provided is 1,446.
How is this so?An apothem is a line from the center of a regular polygon at right angles to any of its sides.
This shape's computation utilizing solely its apothem features several curved bends. To calculate the area, we first divide the octagon into triangles.
We may get the area of the Octagon by multiplying the area of the triangles by the total number.
As a result, the area of the Octagon (A) = (1/2b*h)n.
Where b is the base
height = h
n is the number of triangles.
Remember that the total angle in a circle is 360°, thus if all the triangles are equal, we must divide 360° by 8 triangles to find the angle in each triangle's vertex.
Thus, 360°/8 = 45°
As a result, we obtain the angle of our triangle opposite the base.
Remember that the triangle is divided in two such that each triangle is a right-angled triangle.
As a result, for each right angle triangle, the angle opposite the base is given as:
45°/2 = 22.5°
So we use the rule of tangents to calculate the length of the opposite side (x):
That is to say:
x = 18 Tan 22.5°
= 18 * 0.55785173935
≈ 10.04
As a result, if x equals 10.04, the area of that triangle is
= 1/2 * 10.04 * 18 (which is 1/2bh)
= 90.3792
We may deduce from the foregoing that the Area of the triangle with the Apothem is
= 90.3792 * 2
= 180.74
Recall our formula for finding the area of the octagon:
A = (1/2bh)n
A = (108.74) *8
A = 1,445.95
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To find the area of the regular octagon with center O, divide it into smaller shapes, calculate their areas, and sum them up: (8 * side length^2) + (2 * side length^2 * √2) ≈ 11.3 * side length^2 (rounded to the nearest tenth).
To find the area of a regular octagon with center O, you can divide it into smaller shapes and then sum up their areas.
A regular octagon can be divided into eight congruent isosceles triangles and a square at the center.
Let's assume the side length of the octagon is "s."
Each of the eight isosceles triangles has two equal sides, which are also radii of the octagon, and one base.
The angle between these two radii is 45 degrees because there are 360 degrees in an octagon, and each interior angle of a regular octagon is 135 degrees (360°/8).
This makes each of the two equal angles in the isosceles triangle 67.5 degrees (half of 135 degrees).
You can find the area of one of these isosceles triangles using the formula for the area of a triangle:
Area = (1/2) * base * height
The base is "s," and the height can be calculated using trigonometry:
height = s * sin(67.5 degrees)
Now, you can find the area of one isosceles triangle:
Area of one triangle = (1/2) * s * s * sin(67.5 degrees)
There are eight such triangles in the octagon, so the total area contributed by the triangles is:
Total area of triangles = 8 * (1/2) * s * s * sin(67.5 degrees)
Next, you need to find the area of the square at the center.
The diagonals of this square are equal to the sides of the octagon (s).
The area of the square is:
Area of square = s * s
Now, add the areas of the triangles and the square to find the total area of the octagon:
Total area of octagon = Total area of triangles + Area of square
Total area of octagon = 8 * (1/2) * s * s * sin(67.5 degrees) + s * s.
Now, you can calculate the area of the octagon by plugging in the values:
Total area = 8 * (1/2) * s^2 * sin(67.5 degrees) + s^2
Using the value of sin(67.5 degrees) ≈ 0.9239 (rounded to four decimal places):
Total area ≈ 8 * (1/2) * s^2 * 0.9239 + s^2
Simplify:
Total area ≈ 4 * s^2 * 0.9239 + s^2
Total area ≈ 3.6956s^2 + s^2
Total area ≈ 4.6956s^2
Now, you can round this to the nearest tenth if necessary.
The area of the regular octagon with side length "s" is approximately 4.7s^2 square units.
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Expand the expression
Please help
1/4(36a+b)
Answers
Answer:
9a+b/4
Step-by-step explanation:
Answer:
9a + b/4
Step-by-step explanation:
You must first simplify your answer.