Mathematics College

What is the minimum value of the objective function, C, with the given constraints?

C=2x+3y




A) 2x+3y≤24

B) 3x+y≤15

C) x≥2

D) y≥3

Answers

Answer 1

Given:

The objective function, [tex]C=2x+3y[/tex],

Constraints,

[tex]2x+3y\leq 24[/tex]

[tex]3x+y\leq 15[/tex]

[tex]x\geq 2[/tex]

[tex]y\geq 3[/tex]

To find:

The minimum value of the given objective function.

Solution:

We have,

Objective function, [tex]C=2x+3y[/tex]            ....(i)

The related equations of given constraints are

[tex]2x+3y=24[/tex]       ...(ii)

[tex]3x+y=15[/tex]              ...(iii)

[tex]x=2[/tex], it is a vertical line parallel to y-axis and 2 units left from y-axis.

[tex]y=3[/tex], it is a horizontal line parallel to x-axis and 4 units above from y-axis.

Table of value for (i),

x :   0     12

y :   8     0

Table of value for (ii),

x :   0      5

y :   15     0

Plot these points on a coordinate plane and draw these 4 related lines.

The sign of inequality of [tex]2x+3y\leq 24[/tex] and [tex]3x+y\leq 15[/tex] is ≤, it means the related lines are solid lines and the shaded region lie below the related line.

For [tex]x\geq 2[/tex], left side of the line [tex]x=2[/tex] is shaded.

For [tex]y\geq 3[/tex], shaded region is above the line [tex]y=3[/tex].

From the below graph it is clear that the vertices of the feasible (common shaded region) are (2,3), (4,3), (3,6) and (2,6.667).

Points                     [tex]C=2x+3y[/tex]    

(2,3)                        [tex]C=2(2)+3(3)=4+9=13[/tex]    (Minimum)

(4,3)                        [tex]C=2(4)+3(3)=8+9=17[/tex]    

(3,6)                        [tex]C=2(3)+3(6)=6+18=24[/tex]    

(2,6.667)                 [tex]C=2(2)+3(6.667)=4+20=24[/tex]

Therefore, the objective function is minimum at point (2,3).

What Is The Minimum Value Of The Objective Function, C, With The Given Constraints?C=2x+3yA) 2x+3y24B)

Related Questions

Can someone help me please

Answers

The answer to that is C.

35, 32, 29, 26… what is the 101st term?

Answers

Answer:

-277

Step-by-step explanation:

Answer:

-277?

Step-by-step explanation:


A gumball machine has 6 red gumballs, 3 green
gumballs, and 5 blue gumballs. What is the
probability that the next gumball that comes
out will be red?
A 1/14
B 1/3
C 3/7
D 3/4

Answers

Answer:

D 3/4

Step-by-step explanation:

;)

C 3/7. The total gum balls is 14.
P(red gum ball)= 6/14=3/7
6/14 can be simplified to 3/7 by dividing by 2. 6/2=3. 14/2=7.

P(red gum ball)=3/7

When Jose woke up the temperature was 74°. It

reached a high temperature of 91°. What was

the percent of increase of these temperatures?

Answers

Answer:

22.97

Step-by-step explanation:

Given that,

Initial temperature = 74°

After some time, the new temperature = 91°

We need to find the percent increase in the temperature.

The formula for the percentage increase is given by :

[tex]\%=\dfrac{|\text{final value-initial value}|}{\text{initial value}}\times 100\\\\=\dfrac{91-74}{74}\times100\\\\=22.97\%[/tex]

So, the increase in temperature is 22.97%.

Please help ASAP!! 20 points givin

Answers

Answer:

d or b

Step-by-step explanation:

quick math

Answer is A 5/3
Hope it helps :)

Please help me with this Its kind of frustrating

Answers

Answer:

you have too see what makes 36, 42 ,48 and 27

Step-by-step explanation:

A figure has been dilated from the origin by a scale factor of one seventh. if another dilation from the origin maps the dilated image back
onto the original figure, what is its scale factor?

Answers

Answer:

its scale factor is 3

Step-by-step explanation:

plz mark brainliest

To map the dilated image back  onto the original figure, the scale factor needed is 7.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a factor.

If a figure is dilated from the origin by a scale factor of one seventh, it is given by:

(x, y) ⇒ [(1/7)x, (1/7)y]

To map the dilated image back  onto the original figure, the scale factor needed is 7. Hence:

[(1/7)x, (1/7)y] ⇒ (x, y)

Find out more at: https://brainly.com/question/11707700

PLEASE HELP
I think the answer is either 18 pounds or 26
The scatter plot shows the weight of a baby panda in the months after it is born. How much would you expect a 5 month old baby panda to weigh? ​

Answers

Answer:

Im pretty sure its 21 pounds.

If triangle A B C is congruent to triangle D E F, the measure of angle A equals 55 degrees, and the measure of angle E equals 25 degrees, what is the measure of angle C?
A. 25°
B. 55°
C. 80°
D. 100°

Answers

Answer:

D. 100

Step-by-step explanation:

Answer:

100°

Step-by-step explanation:

Since ΔABC ≅ Δ DEF, and the sum of the measures of the interior angles of a triangle is 180°, subtract the given angle measurements from 180°.

∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F (The vertices are written in this order because they are corresponding angles.)

180° - 55° = 125° - 25° = 100°

∠C is 100°

(A "brainliest" would be nice here! LOL)

I need a little help on this.

Answers

Its answer c) 6
Have a great day

Which quadrilateral has two pairs of equal sides and each pair is a different length?

Answers

Answer:

rectangle hope it helpss

Complete the reminder of the table for the given function rule

Answers

Answer:

1 then -2 then -5

Step-by-step explanation:

It’s in the picture please and thank you ^*

Answers

Answer:

38 degrees

Step-by-step explanation:

3x+2x+15+95+60=360

the sum of the angles of a quadrileteral=360

5x+170=360

5x=360-170

5x=190

x=190/5

x=38 degrees

Select the procedure that can be used to show the converse of the Pythagorean theorem using side links chosen from 3 feet, 4 feet, 5 feet in 6 feet

Answers

Answer: B

Step-by-step explanation:

I got it on Aprx

The 3 feet side and 4 feet side with a right angle between them. Then the 5 feet side will fit to form a right-angle triangle. Then the correct option is B.

What is a Pythagoras theorem?

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Pythagorean theorem using side links chosen from 3 feet, 4 feet, 5 feet in 6 feet.

Then

5² = 3² + 4²

25 = 9 + 16

25 = 25

The 3 feet side and 4 feet side with a right angle between them. Then the 5 feet side will fit to form a right-angle triangle.

Then the correct option is B.

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ2


Given the equation in point slope form y-5=1/2(x+1)

Answers

Answer:

The slope of this equation is 11/2. The point is (1/2, 0)

Step-by-step explanation:

I hope this is the right answer, good luck!

ANSER FOR REAL OR BANHAMMER WILL BE IN YOUR FACE

Answers

Step-by-step explanation:

Since the square is folded along its diagonal,

Perimeter of each triangle

= 2 * Side of square + Diagonal of square.

Side of square

= √(Area of square)

= √(49in²) = 7in.

Diagonal of square

= √(2 * Area of square)

= √(98in²) = 7√2in.

Hence we have 2 * 7in + 7√2in = 7(2 + √2) in.

(Pic provided)
243 is equivalent to...
0 35
94
28
3
Help I’m timed :(

Answers

The answer is A
243 is equivalent to 3^5
Hope that helps

Answer:

The answer is 3⁵

Step-by-step explanation:

3×3×3×3×3

9×9×3

81×3

243

A
Yasmin buys 9 cakes for £10.71. How much does 1 cost?
B
Ben buys 5 pencils for 80p.how much does 1 cost?
C
Maya buys 6 chocolate bars for £3.12. How much does 1 cost?

Answers

Answer:

1.19 is the price for Yasmin.

16p is the cost for Ben.

0.52 is the cost for 1.

Step-by-step explanation:

Divide them all and you will get your answer.

The starting annual salary for an office worker at a company is $29,000. If the company
awards an annual increase of 6.2%, which graph models this situation after the office worker
receives x annual increases?
Office Worker's Salary

Answers

Answer:

On my screen the answer would be A

Step-by-step explanation:

but it could be different for u but I found the answer on Quizizz picture down below

The graph models this situation after the office worker receives x annual increases is to be considered as an option A.

Calculation of the graph model;

Since

The starting annual salary for an office worker at a company is $29,000. If the company awards an annual increase of 6.2%.

So, based on the given graph we can say that The graph models this situation after the office worker receives x annual increases is to be considered as an option A.

Learn more about graph here: https://brainly.com/question/24613103

Pythagorean Theorem Quiz.
1.) Find the unknown side length. Simplify answers that are radicals.
4
3
2.) Find the unknown side length. Simplify answers that are radicals.
16
12

Answers

Answer:

1.) 5              2.) 10.58

Step-by-step explanation:

For each one, you use the equation a^2 + b^2 = c^2 where c is the "hypotenuse"-- the side of the triangle opposite (facing) the right angle which is shown with a small box. The variables a and b do not matter, as long as they are the "legs", the other 2 sides.

So it is 4^2 + 3^2 = c^2 which simplifies to 16+9=25=c^2 and square root both sides and you get c=5

and 12^2 + b^2 = 16^2 which simplifies to 144+ b^2 = 256 and subtract 144 from both sides and you get b^2 = 112 and square root both sides and it is approximately 10.6 :)

What is the equation in point−slope form of the line passing through (−3, −4) and (0, 2)?
Use the table below to answer this question:

x y
0
2
1
−1
2
−6
Find the average rate of change for the given function from x = 0 to x = 2.

Answers

Answer:

The answer is A

Could somebody pls help me with this question

Answers

simplify to 1 hour which will be 6 minutes in 1 hour

in 3 hours it will be 18 minutes

Answer:

18 minutes is the answer

Step-by-step explanation:

•Time couple rested in 2 hrs = 12 min

•Time couple rested in 1 hr = 12/ 2 min = 6min

•Time couple rested in 3 hrs = 6×3 min = 18 min

HOPE IT HELPS YOU

MARK ME AS BRAINIEST

AND YOU CSN THANK ME IN THE COMMENT

What value of n makes the equation true?

Answers

Answer:

-0.7

Step-by-step explanation:

First do 3.2-1.8= 1.4. So now we know that -2n=1.4. Next you solve for n to get the answer of -0.7 with your answer of the third option.

Mark his brainly nowwww

Answers

Answer:

Mark who brainly when?

<3 id.k understand

~

~

~

~

~

´^`

can you find the value x in the f figure​

Answers

Answer:

[tex]x =[/tex] [tex]16\frac{2}{11}[/tex]

Step-by-step explanation:

According to the image, those are verticle angles, so I came up with this equation that can help me solve this problem:

5x+12+6x-10=180

11x+2=180

11x=178

x=[tex]16\frac{2}{11}[/tex]

Aubrey is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $4 each. How much total money would Aubrey have to pay for her family if she were to buy 3 snacks for everybody to share? How much would Aubrey have to pay if she bought x snacks for everybody to share?

Answers

Answer:

$51

Step-by-step explanation:

do 13*3 because of the 2 kids and the adult then add 12 because of the snacks

hope this helps

Answer:

51 and what?

Step-by-step explanation:

3 x 13 = 39                  4 x 3 = 12

39 + 12 = 51

what is x supposed to be, sorry, i suck at variables

What should be done so that the expression will have a value of 10?

12 - 2 + 22 ÷ 8

Add parentheses around 2 + 2.
Add parentheses around 12 - 2.
Add parentheses around 2 2 ÷ 8.
Nothing needs to be done.

Answers

Answer:

Add parentheses around 2 + 2.

Step-by-step explanation:

I’m stuck again on this one

Answers

Answer:

8.7 cm

Step-by-step explanation:

Since all sides of the given shape are equal, so it is a cube.

So length of the diagonal of cube is give as:

[tex]l(diagonal) = l \sqrt{3} \\ \\ = 5 \times 1.732 \\ \\ = 8.66 \\ \\ l(diagonal) \approx8.7 \: cm[/tex]

What is the solution to the system of equations? =6x=y=8 5x+3y = 29 (10,-2) (10, 2) O (2, 10) (-2, 10)​

Answers

Its the 2nd one in the picture

What number could be added to the product of (-7)(-6) so that the sum is equal to 272​

Answers

Answer:

(-7)(-6)=42

272-42=230

Step-by-step explanation:

230 is the answer

Other Questions
What opinion did the United States government have towards Native Americans during the Manifest Destiny era? Name two examples of poor treatment of Native Americans at the hands of the U.S. Government. In the experiment, which of the following variables should remain consistent? the types of plants used the temperature of the water and vinegar the type of soil used All of these choices are correct. what percent of the sun's energy is used by the living organism on eartha. 1% b. 10% c. 20% d. 35% e. 50% The sum of the digits of a positive 2-digit number is 12. The units digit is 3 times the tens digit. Find the number please help! its due today :( could someone he;p me with this worksheet (worth 35 points) plz help ill give brainly For President Wilson, the most important of the Fourteen Points was the one calling forGroup of answer choicesfreedom of the seasDemocratic reformsan independent judiciarya League of Nations If a sample originally had 120 Adams of carbon 14 how many atoms will remain after 17,190 years What is the relationship between an object's mass and its ability to pick up speed, or accelerate? George Washington talked about foreign alliances in his farewell address. How did George Washington feel about foreign alliances? A. He believed alliances were the best chance at protection. B. He did not want to see permanent foreign alliances. C. He only wanted the U.S. to form alliances with European nations. D. He did not want to form alliances with nations already at war. 3,000 is 1/10 of?-300300,0003,00030,000 Question Help;Sheldon can read 8 pages in 15 minutes. Amy can read 16 pages in 1 hour. Explain how you could use a table or graph to find how much longer it would take Amy to read a 320-page book than Sheldon. I need Help please please Jared sells jewelry online he can make 25 necklaces from 375 beads yesterday he made 21 necklaces. How many beads did Jared used to make necklaces yesterday? PLEASE HELP!! Psychology!!Psychologists who study the heritability of intelligence would most like to see if ______ have different intelligencesA. Random Strangers B. Fraternal Twins C. Identical Twins D. Dizygotic Zygotic Twins I WILL GIVE THE BRAINLYEST ANSWER WHO EVER ANSWRS THIS QUICKLY AND CORRECTLY Kiera used her calculator to work out the value of anumber x. She wrote down the first two digits of theanswer on her calculator. She wrote down 7.3.Write down the error interval for x. Write the standard equation of the circle.Ill give brainliest! 2(1 5v) Please help with this i got it wrong twice I need to find the area, what is it? PLs HElp I ONLY HAVE AN HRWhat is the sign of the product (3)(-3)(-2)(4)? (5 points) aPositive, because the products (3)(-3) and (-2)(4) are negative, and the product of two negative numbers is positive bPositive, because the products (3)(-3) and (-2)(4) are positive, and the product of two positive numbers is positive cNegative, because the products (3)(-3) and (-2)(4) are negative, and the product of two negative numbers is negative dNegative, because the products (3)(-3) and (-2)(4) are positive, and the product of two positive numbers is negative