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 me with this question

Answers

A.7 2/3 B.5 1/2 C.3 5/8

What is the correct sequence of steps for calculating 9^6 on the scientific calculator?

First press 9, then 6, then the exponent key, and finally press the equal sign (-).
First press 6, then9, then the exponent key, and finally press the equal sign ().
First press 9, then the exponent key, then 6, and finally press the equal sign (-).

Answers

The answer is Greg !

Answer:

C

Step-by-step explanation:

First press 9, then the exponent key, then 6, and finally press the equal sign.

Determine the slope and the Y-intercept of each linear equation. y = 6x

Answers

Answer:

Slope = 6

Y intercept = 0

Step-by-step explanation:

Given equation is: y = 6x

Equating it with y = mx + b

We find:

Slope m = 6

Y intercept b = 0

there are 36 playing tag at recess. this is 6 times as many playing hopscotch. which model shows this comparison?

i got the top one to the left (checking my answer)

Answers

Answer:

The top left one is correct.

Step-by-step explanation:

We can rewrite this as an algebraic expression simply so it's easier to read.

Let's say hopscotch is [tex]h[/tex]. Tag is 6 times [tex]h[/tex], or [tex]6h[/tex].

That means for every 1 unit of hopscotch, there are 6 units of tag.

The top left one is correct.

PLEASE HELP !!!!! WILL GIVE POINTS !!!!! (√a)=k√a where k=a^n. Find the value of n.

Answers

Answer:

im here for the points

Step-by-step explanation:

im here for the points

Very Short Answer Questions
3. The total surface area of a cube is 1,944 sq cm. Find its side.
35 points and will be mark as brainlist​

Answers

[tex]\huge\bf\underline{Answer}[/tex]

Given :-

Total surface area of a cube = 1944cm²

To Find :-

Side of the cube

Formula :-

[tex]\boxed{\huge \sf{TSA = 6a²}}[/tex]

Where,

TSA = Total surface area of a cube

a = Side of a cube

Solution :-

Let the Side of a cube be 'x'

By substituting values according to the formula,

[tex]\sf{:⇒6(x) ^{2} } = 1944cm^{2} [/tex]

[tex]\sf{:⇒ {x}^{2} = \dfrac{1944}{6} }[/tex]

[tex]\sf{:⇒ {x}^{2} = 324}[/tex]

[tex]\sf{:⇒x = \sqrt{324} }[/tex]

[tex]\sf{:⇒x = 18cm}[/tex]

Hence, The Side of a cube is 18cm

HELP!!! Pleaseeeeeeeeeeeeee

Answers

9514 1404 393

Answer:

  (b)  g(x) = -f(x+3)

Step-by-step explanation:

The dashed-line graph is a reflection over the x-axis and a left-shift by 3 of the solid-line graph. To reflect the function over the x-axis, negate it.

  f(x) ⇒ -f(x) . . . . reflected over the x-axis

To translate a function to the right horizontally by "h" units, replace x in the function with (x-h). Here, we want a left shift, so h=-3. That is, x is replaced by (x+3).

Both transformations together give you ...

  g(x) = -f(x+3)

Estimate 95.63+66.552 by first rounding each number to the nearest whole number

Answers

Answer:

162

Step-by-step explanation:

95.63 rounds up to 96

66.552 stays at 66

96+66=162

Ace gained $ 176 by selling 32 meters cloth for $1496. Find his loss per meters he sold it for $1276​

Answers

Answer:

Selling the total for $ 1276, Ace lost $ 1.37 for each meter.

Step-by-step explanation:

Given that Ace earned $ 176 selling 32 meters of cloth at $ 1496, to find out his loss for each meter if he sold the total for $ 1276, the following calculation must be performed:

1496 - 176 = 1320 (stock price)

1320/32 = 41.25 (price per meter)

1276/32 = 39.87

41.25 - 39.87 = 1.37

Thus, selling the total for $ 1276, Ace lost $ 1.37 for each meter.

can you please help me with this?​

Answers

Answer:

B?

Step-by-step explanation:

I beilieve its B? Ive never heard about dances for inuguration.

the area of a rectangle is 49.7cm2, and the width the rectangle is 3.5 cm what is the length rectangle cenimeters​

Answers

Answer:

Answer = 14. 2

Step-by-step explanation:

Area of rectangle = length x breath

So, area here is = 49.7 cm2

Breath = 3.5 cm

49.7 = length x 3.5

Length = 49.7 ÷ 3.5

Length = 14.2 cm

The perimeter of a rectangle is 120 centimeters. The base is 3 times the height. What are the dimensions of the rectangle? a. h = 9cm, b = 18 cm c. h = 15 cm, b = 45 cm b. h = 19 cm, b = 57 cm d. h = 10 cm, b = 15 cm

Answers

Answer:

[tex]Height = 15[/tex]

[tex]Base = 45[/tex]

Step-by-step explanation:

Given

Shape: Rectangle

[tex]Perimeter = 120cm[/tex]

[tex]Base = 3 * Height[/tex]

Required

Determine the dimensions

The perimeter of a rectangle is:

[tex]Perimeter = 2 * (Base + Height)[/tex]

Substitute 120 for Perimeter

[tex]120 = 2 * (Base + Height)[/tex]

Divide both sides by 2

[tex]60 = Base + Height[/tex]

Substitute 3 * Height for Base

[tex]60 = 3 * Height + Height[/tex]

[tex]60 = 3Height + Height[/tex]

[tex]60 = 4Height[/tex]

Divide both sides by 4

[tex]15 = Height[/tex]

[tex]Height = 15[/tex]

Substitute 15 for Height in [tex]Base = 3 * Height[/tex]

[tex]Base = 3 * 15[/tex]

[tex]Base = 45[/tex]

What is x?
25.12 = 27.10
PLEASE HELP MEEEE

Answers

Answer:

where's the x in the equation?

Answer:

25/12 Therefore, this equation is true: 25/12 = 25/12 If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction. 25/12 = 2 1/12. Simplify Fractions.

need help 8y+3y+9x+4y-5x

Answers

Answer:

4x+15y

Step-by-step explanation:

If you want it simplified

I GIVEEE BRAILILSTTTTTTTT

Answers

Answer:

umumumuykik.iu.fg

Step-by-step explanation:

lui;iou;uyfluylfuy;lui;uy;

You are filling a 2-liter bottle with liquid from full 80-milliliter containers. How many containers will it take to fill the 2-liter bottle?

Answers

Answer:

25 bottles

Step-by-step explanation:

2 litres=2000 milliliters

2000/80=25 (or) 80x25=2000

The amount of containers it will take to fill the 2-liter bottle is 25 containers.

Given the following data:

Volume of bottle = 2 LitersVolume of containers = 80 milliliter

To determine the amount of containers it will take to fill the 2-liter bottle:

In this exercise, you're required to determine the amount of 80-milliliter containers that would be required to fill the 2-liter bottle.

First of all, we would convert the volume in liters to milliliter.

Conversion:

1 Liter = 1000 millimeters

2 Liter = 2000 millimeters

Now, we can find the amount of containers by using the formula:

[tex]Number\;of\;containers = \frac{Volume \;of\;bottle}{Volume \;of\;containers}[/tex]

Substituting the parameters into the formula, we have;

[tex]Number\;of\;containers = \frac{2000}{80}[/tex]

Number of containers = 25 containers

Find more information: https://brainly.com/question/4728821

Giving brainliest. 7th grade math

Answers

yes you got it right hope this helps

In the diagram the radius of the outer circle is 2x cm and the radius of the inner circle is 6 cm. The area of the shaded region is 160

Answers

let's find the area of the outer circle and the inside circle

the inside's circle area

A= π x 6²=36π

the outer's

A' = π x 4x²= 4πx²

A'-A=4πx²- 36π=160πcm² equivalent to x²- 9=40, so x²=49 implies x =sqrt(49)=7, x=7.

Tom bought a pen for $30
and sold it to gain
20% on his cost price. How much money
did he gain?

Answers

Answer:

he gained 6 dollars

Step-by-step explanation:

30 x 0.2

Tom bought a pen for $30 and sold it to gain 20% on his cost price that he gained 6 dollars.

How to calculate unit price of something?

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

Lets suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

It is given that Tom bought a pen for $30 and sold it to gain 20% on his cost price.

Therefore,

30 x 20%

30 x 0.2 = 6 dollars

Thus, he gained 6 dollars.

Hence, Tom bought a pen for $30 and sold it to gain 20% on his cost price that he gained 6 dollars.

Learn more about unit price here:

https://brainly.com/question/945712

#SPJ6

A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 10 insects will die

Answers

Answer:

The probability that exactly 10 insects will die

                     P( X = 10 ) = 0.06385        

Step-by-step explanation:

Step(i):-

Given a certain insecticide kills 60% of all insects in laboratory experiments

Given proportion  p = 0.60

                           q = 1 - 0.60 = 0.40

Given sample size 'n' = 12

Step(ii):-

Let "X' be the random variable of binomial distribution

                              [tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]

The probability that exactly 10 insects will die

                              [tex]P(X=10) = 12_{C_{10} } (0.60)^{10} (0.40)^{12-10}[/tex]

                           

                          [tex]n_{C_{r} } = \frac{n!}{(n-r)!r!} = \frac{12!}{(12-10)!10!} = 66[/tex]

                          [tex]P(X=10) = 66 X (0.60)^{10} (0.40)^{2} = 0.06385[/tex]

Final answer:-

The probability that exactly 10 insects will die

                     P( X = 10 ) = 0.06385        

if a number, n, divided by 8 equals 2.5, what is n?

Answers

Answer:

n is 20

Step-by-step explanation:

If n/8=2.5, then you can just do 8*2.5 to find n. 2.5*8=20

Answer:

n=20 because if you multiple 2.5 and 8 you will get 20 so if you divide 20 and 8 then you get 2.5

algebra 2!! please help im begging. i don’t understand this at all. thank you!

Answers

Answer:

Step-by-step explanation:

so the square root of 6 is the multipyed number of 8 plus 2 divided by9 is to times 8 plus 6

In the figure, x | y and a is a transversal that crosses the
parallel lines.
a
Which angle pair forms alternate exterior angles?
O 24 and 26
O 22 and 28
O 23 and 25
o 22 and 26

Answers

Answer:the answer is b

Step-by-step explanation:

Can someone tell me how to do a transversal angle measurement with steps and angles

Answers

Answer:

Sorry I am not sure but when I figure it out..... I prolly won't

Step-by-step explanation:

Answer:

 

When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles . If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary

Step-by-step explanation:


Find x
27 degrees and 32 degrees will give brainlist

Answers

Answer:

x = 121°

Step-by-step explanation:

If you add up all the angles of a triangle, you get 180°.

So you must add up all the angles.

[tex]27+32+x=180\\\\59+x=180[/tex]

Next you subtract 59 on both sides.

[tex]x=121[/tex]

x should be 121°.

If you would like to check your answer, you can add up 27, 32, and 121. If it all equals to 180, then your answer is correct.

hellllllllllllllllllllllllllllllllllp​

Answers

Answer:

I think it's A. 32.0

Step-by-step explanation:

what’s 100/12 as a mixed number

Answers

Answer: 8 1/3

Step-by-step explanation:

100/12 = 8.33333333

8 4/12

8 1/3

hey please help
just tell me all the ones that work ​

Answers

Answer:

D and A and B i think

Step-by-step explanation:

2(5x+7)=16
what the answer?

Answers

Answer:

x = 1/5

Step-by-step explanation:

2(5x + 7) = 16

2 * 5x + 2 * 7 = 16

10x + 14 = 16

10x = 16 - 14

10x = 2

x = 2/10

x = 1/5

what assumption have you made in answering part b​

Answers

You're assuming that this data set represents all of Mrs. Hassaan's pupils. Certain students could be missing from the histogram - for instance, there could be one or two students who missed the test, but for certain reasons will be taking a make-up exam. Their grade would not be recording in this data set, but they still contribute to the class size, and so would be unaccounted for here.

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