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

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.

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

Answers

Answer:

-277

Step-by-step explanation:

Answer:

-277?

Step-by-step explanation:

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)

Mark his brainly nowwww

Answers

Answer:

Mark who brainly when?

<3 id.k understand

~

~

~

~

~

´^`

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 :)

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:

(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.

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

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

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]


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!

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%.

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.

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

Complete the reminder of the table for the given function rule

Answers

Answer:

1 then -2 then -5

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

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]

Can someone help me please

Answers

The answer to that is C.

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:

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

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

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 :)

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

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.

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

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

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

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