Convert the problem to standard form and write the initial tableau with slack variables:
Maximize
[tex]Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6[/tex]
Subject to:
[tex]x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000[/tex]
All variables are non-negative.
Tableau
x1 x2 x3 x4 x5 x6 s1 s2 b
Z -3 -3 7 6 18 14 0 0 0
s1 1 1 0 0 0 0 1 0 4000
s2 3 3 3 3 3 2 0 1 6000
x5 0 0 1 0 1/3 0 0 0 0
x6 0 0 0 1 0 1/2 0 0 0
The basic variables are s1, s2, x5, and x6.
Step 1: Choose entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.
Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,
corresponding to s1. s1 leaves the basis.
Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.
x1 x2 x3 x4 x5 x6 s1 s2 b
Z -3 -3 7 6 18 14 0 0 0
x5 0 0 1 0 1/3 0 0 0 0
s2 3 3 3 3 2 2/3 2/3 0 1/3 24000
x3 1 0 1/3 0 1/3 0 -1/3 0 0
x4 0 1 0 1/3 0 1/2 -1/6 0 0
The basic variables are x5, x3, x4, and s2.
Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.
Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.
As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.
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Maria is renting kayaks from a local shop that charges a $7 fee, plus an hourly rate of $5. 50. For how long can maria rent the kayak if she pays a total of $40?.
The number of hours Maria rent the kayak for the paid amount of $40 when hourly rate is $5.50 is equal to 6 hours.
Fees of renting charges paid for kayaks from a local shop = $7
Hourly rate = $5.50
Let 't' be the number of hours Maria rent kayak.
Total fees paid by Maria for renting kayak for 't' hours is equal to $40
Required equation to represents the above condition is
$40 = $7 + $5.50t
Simplify the expression to get the value of 't'
⇒ 5.50t = 40 - 7
⇒ t = 33 / 5.50
⇒ t = 6 hours
Therefore, for the number of hours Maria rent kayak by paying total of $40 is equal to 6 hours.
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need help pls Choose ALL answers that describe the quadrilateral
Answer: A. Parallelogram
Step-by-step explanation: A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length.
(ej a number is divisible by 2 and 3, it is divisible by 6. 64 is divisible by 2 but no Sh
What can be concluded from this?
64 is also divisible by 3
54 s dvisible only by 2
() 64 is also divisible by 6
(v) 64 is not divisite by 6
Answer:
64 is not divisible by 6 because although it is divisible by 2, it is not divisible by 3 so it is not divisible by 6.
Step-by-step explanation:
Graph the function y=x/4
Answer:
Step-by-step explanation:
Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 232.36 square inches.
If the diameter of the tub is 8 inches, what is its height? Use π = 3.14.
6.75 inches
5.25 inches
3.375 inches
2.625 inches
If the diameter of the tub is 8 inches, then the height of gallon tube is, 5.25 inches
What is surface area ?Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.
The surface area of a cylinder can be expressed as:
SA = 2πr² + 2πr x h
where r is the radius of the cylinder, h is its height, and π is the constant pi (3.14).
The diameter of the tub is 8 inches, which means the radius is 4 inches. We are also given that the total surface area is 232.36 square inches.
So we can write:
232.36 = 2(3.14)(4²) + 2(3.14)(4)(h)
Simplifying and solving for h, we get:
232.36 = 100.48 + 25.12h
131.88 = 25.12h
h = 131.88/25.12
h ≈ 5.25 inches
Therefore, the height of the ice cream tub is approximately 5.25 inches.
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Translate the sentence into a mathematical equation.
Power equals current times voltage.
Let P represent power, current, and V voltage. Write the equation.
P=
On solving the Power equals Current times voltage as an equation we get power is P = VI
What is equation?A mathematical equation is a fοrmula that joins twο statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences οn either side of a letter is described by a mathematical fοrmula. Often, there is only οne variable, which also serves as the symbol. fοr instance, 2x – 4 = 2.
Given to write
Power equals current times voltage
in mathematical equation, i.e.
P = V × I
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If AB = 12 and BC = 19,
then what does AC equal?
The value of length AC is,
⇒ AC = 31
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
The lengths are,
AB = 12 and BC = 19
Now, If the points A, B and C are colinear.
Then, The value of length AC is,
⇒ AC = AB + BC
⇒ AC = 12 + 19
⇒ AC = 31
Thus, We get;
⇒ AC = 31
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Help!!
Write an equation to show the total cost, y, for x months.
help me please i need help
Answer:
Step-by-step explanation:
The ansewr is C
Answer: 523.3cm^3
Step By Step Explanation:-The volume of a sphere can be calculated using the formula:
V = (4/3) * π * r^3
where r is the radius of the sphere. The diameter of the sphere is 10 cm, so the radius is half of that, or 5 cm.
Substituting the radius into the formula, we get:
V = (4/3) * π * (5 cm)^3
= (4/3) * π * 125 cm^3
= approximately 523.6 cm^3
So, the closest measurement to the volume of the sphere in cubic centimeters is approximately 523.3 cm^3.
In fall 2006, Pace University in New York raised its annual tuition from $25,000 to $29,750. Freshman enrollment declined from 1,475 in fall 2005 to 1,130 in fall 2006. Assuming that the demand curve for places in the freshmen class at Pace did not shift between 2005 and 2006, use this information to calculate the price elasticity of demand LOADING... . Use the midpoint formula in your calculation.
Answer:The answer is 20000
Step-by-step explanation:
The sum of two numbers is 42. The smaller number is 16 less than the larger number. What are the numbers?
Larger number:
Smaller number:
Answer:
Larger number: 29
Smaller number: 13
Step-by-step explanation:
29 + 13 = 42
29 - 16 = 13
Answer:
Larger number: 29
Smaller number: 13
Step-by-step explanation:
x = larger number
y = smaller number
x+y=42
29-13 = 16
29+13=42
A passenger train traveled 240 miles in the same amount of time it took a freight train to travel 160 miles. The rate of the freight train was 20 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
The rate of the passenger's train is given as follows:
60 miles per hour.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
For the passenger train, the equation is given as follows:
v = 240/t.
vt = 240
t = 240/v.
For the freight train, the velocity is 20 miles slower than for the passenger train, hence:
v - 20 = 160/t
v = 160/t + 20.
Replacing the first equation into the second, the rate of the passenger train is obtained as follows:
v = 160v/240 + 20
v = 2v/3 + 20
v/3 = 20
v = 60 miles per hour.
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what is the solution to | x | -2 <= -3
Riding equation of the line that has the same slope as 3X minus 2Y equals 12 in the same y-intercept as 5Y +21 equals 4X
The linear equation can be written as:
y = (3/2)*x - 21/5
How to write the linear equation?
A general linear equation can be written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
First, we know that our line has the same slope than:
3x - 2y = 12
Rewriting that we will get:
3x - 2y = 12
3x - 12 = 2y
(3/2)x - 12/2 = y
So the slope of this line is (3/2).
And our lie has the same y-intercept as 5y + 21 = 4x
We can rewrite that to get:
5y = 4x - 21
y = (4/5)x - 21/5
The y-intercept is -21/5
Then the linear equation is:
y = (3/2)*x - 21/5
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12. The point M(-6, -4) is translated 2 units right. What are the coordinates of the resulting point, M'?
(-4,0)
(2,-4)
(-4,-2)
(-4,-4)
Answer:
(-4,-2)
Step-by-step explanation:
Answer: (-4,-4)
Step-by-step explanation: the y- coordinate stays the same you would have to move the x-coordinate only which would give you -4. Because you are adding 2 to -6.
Erica built a fort out of big foam blocks that are 1 /4 of a foot tall. She is adding a 5-foot tower to one side of the fort. How many blocks tall will the tower be?
By the equation formed by the relation to build 5 feet tall tower, Erica will need 20 bricks.
What is an equation?
An equation is a mathematical statement consisting of two expressions joined by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation gives the value of the variable x as x = 7.
According to the information given in the question:
1 brick = 1/4 Feet
Which means, 4 bricks = 1 feet
As Erica wants to make 5 feet tall tower,
5 feet tower = 5 x 4
= 20 bricks
Hence, Erica will need 20 bricks to build 5 feet tower.
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What is the volume 
The volume of the composite figure is 2592 cubic feet.
What is composite figure?The area that any composite shape covers is known as the area of composite shapes. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These shapes or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.
The volume of the figure = Volume of the mounted object + Volume of the base object.
The volume of the mounted object is:
V = (l)(b)(h)
V = (9)(12)(6)
V = 648 cubic feet.
The volume of the base object is:
V = (l)(b)(h)
V = (27)(12)(6)
V = 1944 cubic feet.
The total volume of the composite figure is:
V = 648 + 1944
V = 2592 cubic feet
Hence, the volume of the composite figure is 2592 cubic feet.
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Help!! Drag and drop a statement or reason to each box to complete the proof.
Given: PQ≅PR
Prove: ∠Q≅∠R
The triangles ΔPQM and ΔPRM are congruent. Then angle Q is identical to angle R.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The line segment PM is the median of the isosceles triangle ΔPQR.
Point M is the midpoint of QR by the definition of the median.
In triangles ΔPQM and ΔPRM, then we have
PQ = PR {Given}
QM = RM {Mid point}
MP = MP {Reflexive property}
The triangles ΔPQM and ΔPRM are congruent to each other by SSS postulates.
∠Q = ∠R
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The complete question is given below.
The line segment PM is the median of the isosceles triangle ΔPQR. Drag and drop a statement or reason to each box to complete the proof.
Given: PQ ≅ PR
Prove: ∠Q ≅ ∠R
An investment of $65,000 is increasing at a rate of 3.2% per year. Which function represents how to find the value of the investment after t years?
Answer:
I honestly don't know I just need points
Use the information provided to answer Part A through Part D.
One method that can be used to prove that the diagonals of a parallelogram bisect
each other is shown in the given partial proof.
S
ven: Quadrilateral PQRS is a parallelogram
ove:
PT= RT
ST= QT
1.
2.
7.
3.
4.
Statements
Quadrilateral PQRS is a
parallelogram
PQ || SR
PS || QR
ZPQS = ZRSQ
ZQPR ZSRP
?
5. ASRT AQPT
6.
PT=RT
ST=QT
Q
I
R
PT = RT
ST=QT
1. Given
2. Definition of
parallelogram
3.
4.
5.
Reasons
6.
2
?
Opposite sides of a
parallelogram are
congruent
?
Corresponding par
of congruent
triangles are
congruent
7. Definition of
congruent line
erop segments
Answer:
the anwser is 5
Step-by-step explanation: 5
A scientist collected a sample of data on cactus heights. the data were rounded to the nearest foot. if the minimum score was 4 feet and the range was 6 feet, what was the maximum score? The answer is 9.
I found this question here on brainly but an expert said the answer is 10 but that is wrong. I tried commenting to say that the answer is 9 but couldn't figure out how to comment so I just posted this question with the answer for anyone who needs the answer. :) The answer is 9, I received points for it being correct.
Answer: the maximum score was 10 feet.
Step-by-step explanation:
here's a step-by-step explanation:
Identify the minimum score: The minimum score is given in the problem as 4 feet.
Identify the range: The range is also given in the problem as 6 feet.
Calculate the maximum score: To find the maximum score, we simply need to add the minimum score and the range.
Maximum score = Minimum score + Range
Maximum score = 4 feet + 6 feet
Maximum score = 10 feet
So the maximum score was 10 feet.
Leager
Assessment Items
Question
A researcher found that for the years 2013 to 2019, the equation, y=-0.4(2-3)² + 42,
models the average gas mileage of new vehicles sold in Switzerland, where z is the
number of years since 2013 and y is the average gas mileage, in miles per gallon (mpg).
During what year was the average gas mileage for new vehicles sold in Switzerland the
greatest?
2016 is the year in which the average gas mileage is the greatest.
What is an equation?An equation contains one or more variables connected by an equal sign.
Example:
1x + 2 = 99 is an equation.
We have,
y = -0.4 (x - 3)² + 42
where x = the number of years since 2013.
y = average gas mileage
Now,
In 2016,
x = 3
y = -0.4 (3 - 3)² + 42
y = 0 + 42
y = 42
This is the greatest value for any x value.
Thus,
In 2016, the average gas mileage for new vehicles sold is the greatest.
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When she subtracts 4 from both sides, 1/2x = -1/2x
results. What is the value of x?
Answer: 0
Step-by-step explanation:
1/2x = -1/2x cannot be true for any other value of x except when x equals 0. In other words, we need the left and right sides to equal each other, but that would only happen when x=0.
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 2.2 cubic feet of water weigh:
In pounds?
In tons?
So far I Havn't received the correct answer yet.
Determine the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as Tor F.
1.∃x∀y(xy = 0)
2. ∃x (x^2 = -1)
The truth value for the logical proposition is 1) T 2) F 3) T 4) F 5) T
The rules of mathematical logic specify methods of reasoning mathematical statements. Greek philosopher, Aristotle, was the pioneer of logical reasoning. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. It has many practical applications in computer science like the design of computing machines, artificial intelligence, the definition of data structures for programming languages etc.
Propositional Logic is concerned with statements to which the truth values, “true” and “false”, can be assigned. The purpose is to analyze these statements either individually or in a composite manner
the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as T or F.
1) there exists x for all y xy=0 is true T
2) there exist x x2=-1 F
3) for all x2=y T
4) for all x there exist x=y2 F
5) for all x not equal to zero xy=1 T
The complete question is -
the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as T or F.
1) there exists x for all y xy=0 is true
2) there exist x x2=-1
3) for all x2=y
4) for all x there exist x=y2
5) for all x not equal to zero xy=1
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A set contains the numbers 0,6,12 and 15. 2 different numbers are selected randomly from this set. What is the probability that the sum is greater than 12
Answer:
Step-by-step explanation:
To find the probability of the sum of two randomly selected numbers from a set being greater than 12, we need to first find the total number of possible combinations of two numbers and then count the number of combinations that result in a sum greater than 12.
The set contains four numbers, so there are 4 choose 2 possible combinations of two numbers, which is equal to (4! / (2! * (4 - 2)!)), or 6 combinations. These combinations are:
(0,6), (0,12), (0,15), (6,12), (6,15), (12,15)
Next, we'll count the number of combinations that result in a sum greater than 12. These combinations are:
(6,15), (12,15)
There are 2 combinations that result in a sum greater than 12.
Finally, to find the probability, we'll divide the number of favorable outcomes (combinations with a sum greater than 12) by the total number of outcomes (all possible combinations of two numbers), and express the result as a fraction:
probability = 2 / 6
Reducing the fraction, we get:
probability = 1 / 3
So, the probability that the sum of two randomly selected numbers from the set is greater than 12 is 1/3.
That's how you find the probability of the sum of two randomly selected numbers from a set being greater than a certain value. By counting the number of favorable outcomes and dividing by the total number of possible outcomes, you can find the probability of a certain event.
On a partagé une somme entre trois personnes: la première en a reçu les deux tiers, la deuxième 300dirhams de moins que la deuxième. Chercher la somme et les trois parts
Find the angle of elevation
from point C to point A.
590
m
402 m
2
nm
B
Angle of elevation = [ ? ]0
The required angle of the elevation at point C to A is given as ∠C = 31°.
What is the angle of elevation?The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards to an object or point. In other words, it is the angle between the horizontal and an observer's line of sight to an object above the observer
Here,
A figure has been shown, Consider triangle ABC, where ∠A = 59, ∠B = 90°,
Since the sum of the angle in the triangle should be 180°.
∠A + ∠B + ∠C = 180
∠C + 90 + 59 = 180
∠C = 90 - 59
∠C = 31°
Thus, the required angle of the elevation at point C to A is given as ∠C = 31°.
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Which number line best represents the solution to the inequality 3x+2≤4x+5≤9
?
The number line of the inequality is (d)
How to determine the number line of the inequalityfrom the question, we have the following parameters that can be used in our computation:
3x+2≤4x+5≤9
When this is expanded, we have
3x + 2 ≤ 4x + 5 and 4x + 5 ≤ 9
Evaluate the like terms
So, we have the following representation
-x ≤ 3 and 4x ≤ 4
Divide by the coefficient of x
x ≥ -3 and x ≤ 1
When combined, we have
-3 ≤ x ≤ 1
So x is between -3 and 1, inclusive.
This is represented by the number line (d)
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5 redused to lowest terms make it easy kid friendly for my 10 year old equation please
Sure! To reduce the fraction 5 to its lowest terms, we need to find the greatest common factor of 5 and divide both the numerator and denominator by it.
The greatest common factor of 5 and 5 is 5, so we divide both the numerator and denominator by 5 to get:
5 / 5 = 1
So, 5 reduced to its lowest terms is 1.
To make it kid-friendly, you could explain it like this: "We can simplify the fraction 5 by dividing the top and bottom by the biggest number that they both share. In this case, 5 is the biggest number that 5 and 5 share, so we divide both 5 and 5 by 5 to get 1."
