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Find the maximum value of
C = 3x + 2y
Subject to the following constraints:
x > 0
y>0
x + 3y <15
4x + y <16
Enter
Answers
Answer:
Given:
x > 0
y > 0
And,
x + 3y < 15
4x + y < 16
<=>
4x + 12y < 60
4x + y < 16
<=>
11y < 44
<=> y < 4
Otherwise
x + 3y < 15
4x + y < 16
<=>
x + 3y < 15
12x + 3y < 48
<=>
11x < 33
<=>
x < 3
=> C = 3x + 2y < 3*3 + 2*4 = 9 + 8 = 17
=> C < 17
Hope this helps!
:)
The maximum value of C is an illustration of objective functions
The maximum value of C is 25
The objective function is given as:
[tex]\mathbf{C = 3x + 2y}[/tex]
The constraints are:
[tex]\mathbf{x + 3y < 15}[/tex]
[tex]\mathbf{4x + y < 16}[/tex]
[tex]\mathbf{x,y > 0}[/tex]
Plot the graphs of the constraints
From the graph (see attachment), the only optimal point is (3,4)
Substitute 3 for x and 4 for y in the objective function.
So, we have:
[tex]\mathbf{C = 3x + 2y}[/tex]
[tex]\mathbf{C = 3(3) + 2(4)}[/tex]
[tex]\mathbf{C = 9 + 8}[/tex]
[tex]\mathbf{C = 17}[/tex]
Hence, the maximum value of C is 17
Read more about optimizing functions at:
https://brainly.com/question/14778650
Related Questions
The base of a rectangular prism has an area of 13 2/3, and the height of the prism is 8 5/6. What is the volume of the prism? Be sure to use this format: whole number numerator/denominator.
Answers
Answer:
120 [tex]\frac{13}{18}[/tex]
Step-by-step explanation:
The formula for finding the volume of a prism is:
V = Bh
You have to convert 13 [tex]\frac{2}{3}[/tex] into an improper fraction, like so:
[tex]\frac{41}{3}[/tex]
Convert the other:
[tex]\frac{53}{6}[/tex]
Multiply:
[tex]\frac{41}{3}[/tex] · [tex]\frac{53}{6}[/tex] = [tex]\frac{2173}{18}[/tex]
Convert to mixed fraction:
120 [tex]\frac{13}{18}[/tex]
Henry starts the day with $30. He and his sister go to the fair. He pays for his own admission of $10,but fails to notice that $15 falls out of his wallet while he is paying. His sister lends him $10 so that he can still enjoy the fair. Write the equation that illustrates his day’s financial events.
Answers
Answer:
30-10-15+10
Step-by-step explanation:
Answer:
15 is the awnser
Step-by-step explanation:
30-10-15+10=15
Math question down below
Answers
Answer:
12 large books
Step-by-step explanation:
Simplify, using the distributive property and then combining like terms. 5c+2(10−c)
Answers
Answer:
3c +20
Step-by-step explanation:
5c+2(10−c)
Distribute
5c+ 20 -2c
Combine like terms
3c +20
Answer:3c+20
Step-by-step explanation:
Distribute
5c+(2)(10)+(2)(-c)
5c+20+-2c
Combine Like Terms:
(5c+-2c)+(20)
3c+20
Hope I helped:)
What is the surface area, in square inches, of the
sphere shown below? (SA = 4.0) (pi ≈ 1 3.14)
а. 530.7 sq in.
b. 2122.6 sq in.
с. 4245.3 sq in.
d. 9203 sq in.
Answers
Answer:
hey if you still need the i have them all just finished the test
Step-by-step explanation:
need help again lol plz
Answers
b) >
c) =
girl this is easy
What is the solution to the equation sqrt5X-7= sqrt3X+5?
x = 1
x = 6
x = 12
x = 24
Answers
Answer:
X=6
Steps are in the picture
Find m Just trying to get my credit
Answers
Answer:
130
Step-by-step explanation:
2x+5x+5=180
7x+5=180
7x=175
x=25
5(25)+5=125+5=130
Answer:
∠ABC=130
Step-by-step explanation:
2x+5x+5=180
7x=180-5
7x=175
x=25
∠ABC=5*25+5=130
Need help with this
Answers
Answer:
5 to the power of -2
Step by Step explanation:
Because you are diving, you need to subtract the powers.
For example, you subtract 10 from 12 to get -2
The 5 remains the same so the answer should be 5 to the power of -2
Hope this helps
complete the square to form a perfect-square trinomial.
2. x^2 - 4x + ?
4. x^2 + 12x + ?
6. x^2 + 18x + ?
(just tell me what the number is for the ? on each problem.)
Answers
Look at the attached picture
Hope it will help you.
Good luck on your assignment
please help me! thank you
Answers
Answer:
13 pounds happy to help mark me as brainliest pls!!!
Step-by-step explanation:
Given the line 2 x - 3 y - 5 = 0, find the slope of a line that is perpendicular to this line. A.3/2
B.2/3
C.- 3/2
Answers
Answer:
Step-by-step explanation:
2x - 3y = 5
-3y = -2x + 5
y = (2/3)x - 5
the perpendicular slope is -3/2
the answer is c
Answer:
the perpendicular slope is -3/2
Step-by-step explanation:
Reasoning in a laboratory, the probability a bacterial colony thrives is 70%. The numbers 0 to 6 represent the outcome that a colony thrives. The numbers 7 to 9 represent the outcomes that a colony does not thrive. The list of random numbers simulates the out comes of 4 colonies . Based On the simulation in 6 trails . what is the probability that exactly half of the colonies will thrive.
4285 6903 3829 7871 2868 5137
Answers
Answer:
The probability that exactly half of the colonies will thrive = (1/3) = 0.3333
Step-by-step explanation:
The list of random numbers simulates the out comes of 4 colonies.
Based On the simulation in 6 trails, what is the probability that exactly half of the colonies will thrive?
The probability of an event is given mathematically as the number of elements in the event divided the total number of elements in the sample space.
Noting that the numbers 0 to 6 indicate that a colony thrives and the number 7 to 9 represent that a colony doesn't thrive.
The 6 trials are given as
4285; 3 colonies thrive, 1 doesn't.
6903; 3 colonies thrive, 1 doesn't.
3829; 2 colonies thrive, 2 don't.
7871; 1 colony thrives, 3 don't.
2868; 2 colonies thrive, 2 don't.
5137; 3 colonies thrive, 1 doesn't.
The number of trials where exactly 2 colonies thrive = 2
The total number of trials = 6
The probability that exactly half of the colonies will thrive = (2/6) = (1/3) = 0.3333
Hope this Helps!!!
Write the number in standard form. 6.45×10^−4
Answers
Answer:
.000645
Step-by-step explanation:
.0006.45
move the decimal place 4 places to the Left because it is a negative.
Select the equation that represents the graph below.
Answers
Answer:
D)
Step-by-step explanation:
The y intercept is at 3 and it goes up 3 over 2. and since its going up its positive. Remember rise over run.
Answer:
D
Step-by-step explanation:
Slope: 3/2
y-intercept:3
x,y
0,3
2,6
Which of these graphs represents a function
A.w
B.x
C.y
D.z
Answers
The correct option is D. The graph z is representing a quadratic function.
What is a quadratic function?In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
The general form of the quadratic functions is represented as below:-
y = ax² + bx + c
Where a,b, and c are the constants x and y are variables.
The graph of the quadratic functions will be parabolic on the x-y plane.
Therefore, the correct option is D. The graph z is representing a quadratic function.
To know more about a quadratic function follow
https://brainly.com/question/7784687
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what line represents the relationship between r and s shown in the table r 0,1,2,3 s 10,11,12,13
Answers
Answer:4/13
Step-by-step explanation:
what does the numerator of the fraction 10/6 mean?
Answers
Answer:
6
Step-by-step explanation:
If Kevin wants a 90 average in math after 5 tests and his first 4 tests are 76, 92, 89 and 97 what does he need on the fifth test for a 90 average?
Answers
Solving for the average is simple:
Add up all of the exam scores and divide that number by the number of exams you took.
(87 + 88 + 92) / 3 = your average if you didn't count that fourth exam.
Since you know you have that fourth exam, just substitute it into the total value as an unknown, X:
(87 + 88 + 92 + X) / 4 = 90
Now you need to solve for X, the unknown:
87
+
88
+
92
+
X
4
(4) = 90 (4)
Multiplying for four on each side cancels out the fraction.
So now you have:
87 + 88 + 92 + X = 360
This can be simplified as:
267 + X = 360
Negating the 267 on each side will isolate the X value, and give you your final answer:
X = 93
Now that you have an answer, ask yourself, "does it make sense?"
I say that it does, because there were two tests that were below average, and one that was just slightly above average. So, it makes sense that you'd want to have a higher-ish test score on the fourth exam.
current count = 4
current sum = 76+92+89+97=354
we need average = 90 = sum/5
so, we need sum = 90*5=450
To get sum 450, he needs to score 450-354=96 on his best test.
Now, (76+92+89+97+96)/5=90
find the vertex of the parabola represented by the function f(x)= -2x^2
Answers
The vertex of this parabola is the origin or, (0 , 0)
Hope this helps !
1) write down a different ratio equivalent to 12 : 3
2) write down a different ratio equivalent to 30 : 24
Answers
2) 60:48
I just multiplied by 2
Answer: 1) 4:1 2) 60/48
Step-by-step explanation:
1. 12: 3 is the same as 12/3 so you can diving both side by 3.
12:3 ÷ 3/3=4/1
2. 30:24 is the same as 30/24 so you can divide both sides by 6 or multiply both sides by 2.
30/24 * 2/2= 60/48
In the similar quadrilaterals below, what is the length of AB
10 cm
2.5 cm
8 cm
3 cm
Answers
Answer:
Side AB is 10 cm.
Step-by-step explanation:
The given quadrilaterals ABCD and EFGH are similar.
From the given figure, we can observe the following angles and sides are corresponding.
[tex]\angle A = \angle E=90^\circ\\\angle B = \angle F=63^\circ\\\angle C = \angle G=117^\circ\\\angle D = \angle H=90^\circ[/tex]
Ratio of corresponding sides will be equal:
AB:EF = BC: FG = CD:GH = DA:HE
We have to find the side AB.
Given the sides
EF = 5 cm
BC = 9 cm
DA = 8 cm
EH = 4 cm
So, ratio DA:EH = 8:4 = 2:1
We know that ratio of corresponding sides will be same:
AB:EF = DA:EH
[tex]\Rightarrow \dfrac{AB}{5} = \dfrac{2}{1}\\\Rightarrow AB = 10 cm[/tex]
So, side AB is 10 cm.
The one-to-one functions g and h are defined as follows.
=g, , −7 1, , −4− 8, , 6 7 , 7− 3
=hx−2x3
Find the following
Answers
Answer:
g^−1(7) = 6
h^−1(x) = x/2 + 3/2
(h^−1 ∘ h)(3) = 3
Step-by-step explanation:
If
g(6) = 7
Then
g^−1(7) = 6
h(x) = 2x - 3
Isolate x:
2x = h(x) + 3
x = h(x)/2 + 3/2
Replace x with h^−1(x) and h(x) with x:
h^−1(x) = x/2 + 3/2
We know that:
(h^−1 ∘ h)(x) = x
then:
(h^−1 ∘ h)(3) = 3
Which is the longest length?
a 1 yd. 20 in.
b 1yd. 1 ft.
С
40 in.
d 3 ft.
Answers
Answer:
a-1yd20in
Step-by-step explanation:
a-4ft 8in
b-4ft
c-3ft 4in
d-3ft
Answer:
it's A, one yard and 20 inches
Step-by-step explanation:
If you convert them all to inches, a yard and a 20 inches are equal to 56 inches, so you can rule out the 40 inches answer. a yard and a foot are equal to 48 inches, so we can rule out that also. 3 feet is equal to 36 inches, because we know that a foot is equal to 12 inches. so you are left with A. 1 yard and 20 inches.
Suppose f(x) =
[tex] {x}^{2} [/tex]
. What is the graph of g(x)=1/2f(x)?
Answers
Answer:
It's D.
Step-by-step explanation:
The 1/2 stretches the graph horizontally of x^2 by a factor 1/2.
Option-D will represent the required graph of the function [tex]g(x) = \frac{1}{2}f(x)[/tex].
What is a function?"A function is defined as a relation between a set of inputs having one output each."
The given function:
[tex]f(x) = x^{2}[/tex]
Therefore the required function is:
[tex]g(x)\\= \frac{1}{2}f(x)\\= \frac{1}{2}x^{2}[/tex]
By putting the values of 'x' as -2, -1, 0, 1, 2 etc. we get:
[tex]g(-2) = (-2)^{2} = 4\\ g(-1) = (-1)^{2} = 1\\ g(0) = (0)^{2} = 0\\ g(1) = (1)^{2} = 1\\ g(2) = (2)^{2} = 4[/tex]
By plotting this value, we get option-D is the graph that represents the function g(x).
Learn more about a function here: https://brainly.com/question/12251916
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5 CR
UTION
Abed says he has written a system of two linear equations that has an infinite number of solutions. One of the
equations of the system is y = 3x – 1. Which could be the other equation?
y = 3x + 2
3x - y = 2
3x - y = 1
3x + y = 1
Done
Answers
Answer:
3x - y = 1
Step-by-step explanation:
The system:
[tex]$\left \{ {{y = 3x -1} \atop {y = 3x + 2}} \right. $[/tex]
There is no solution to this system of equations.
The system:
[tex]$\left \{ {{y = 3x -1} \atop {3x - y = 2}} \right. $[/tex]
[tex]$\left \{ {{y = 3x -1} \atop { y = 3x-2}} \right. $[/tex]
The is one solution to this system.
The system:
[tex]$\left \{ {{y = 3x -1} \atop {3x - y = 1}} \right. $[/tex]
[tex]$\left \{ {{y = 3x -1} \atop { y = 3x-1}} \right. $[/tex]
There are infinity solutions to the system.
The system:
[tex]$\left \{ {{y = 3x -1} \atop {3x + y = 1} \right. $[/tex]
[tex]$\left \{ {{y = 3x -1} \atop { y = 1-3x}} \right. $[/tex]
The is one solution to this system.
PLEASE HELP ME
I NEED IT
Answers
Answer:
[tex]\sqrt{24}[/tex]
Step-by-step explanation:
[tex]4\frac{4}{9}[/tex] cannot be correct because it equals 4.4.
[tex]\sqrt{20}[/tex] cannot be correct because it equals 4.5.
480% is 480/100 which equals 4.8 which is also not correct.
Therefore, [tex]\sqrt{24\\}[/tex] is correct because it is greater than 4.8 and less than 5.0.
Is this SAS or Not SAS?
Answers
the special assault squad or the SAS where oppressive soldiers sent from england to murder irish people for fighting for freedom
It costs Trevor $50 to have a security system installed in his house. He pays a monthly service fee plus tax of 6% of his monthly bill. After 6 months, Trevor had paid a total of $361.64 for his service fee, taxes, and his initial installation. Trevor’s monthly service fee, not including taxes, is ___.
Answers
Answer:
$49
Step-by-step explanation:
Cost of security system installation = $50
Let the monthly service cost be $x
In 6 month monthly service cost = 6*$x= $6xtax percentage = 6% of monthly service cost
hence if monthly service cost is $x
Then Tax value in terms of x is = 6% of $x = 6/100 * $x =$ 0.06x
In 6 month, Tax value in terms of x = 6 * $0.06x = $.36x_______________________________________________
Therefore total cost incurred by Trevor in 6 month including installation charges =
6 month monthly service cost + Tax value in 6 month + installation cost
Substituting value of 6 month monthly service cost , Tax value in 6 month , installation cost in above expression we have
Therefore total cost incurred by Trevor in 6 month including installation charges = $6x+ $0.36x+ $50 = $6.36x + $50
But it is given that After 6 months, Trevor had paid a total of $361.64 for his service fee, taxes, and his initial installation
Therefore total cost incurred by Trevor in 6 month including installation charges is also equal to $361.64
Hence,
$6.36x + $50 = $361.64
=> $6.36x = $361.64 - $50
=>$6.36x = $311.64
=> x = $311.64/6.36
=> x = 49.
Therefore , Trevor’s monthly service fee, not including taxes is $X which is equal to $49.
Dustin works in a department store. He earned $89.00 for working 10 hours last week. At this rate, how much would Dustin earn for working 38 hours?
Answers
Answer:
$338.20
Step-by-step explanation:
Find out how much Dustin gets for one hour of work, since you are given how much Dustin earns in 10 hours, you divide it by 10 (the number of hours) to find one hour,
89/10=8.9
$8.9 per hour
So 38 hours would be
8.9 x 38= $338.20
Answer:
$338.20
Step-by-step explanation:
