A furniture manufacturer makes two types of furniture: chairs and sofas. The production of the sofas and chairs requires three operations: carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The prfit per chair is $90 and the profit per sofa is $75. The manufacturer wants to know how many chairs and how many sofas should be produced each day to maximize the profit.
Formulate a linear programming (LP)problem you would use to find a solution.

Answers

Answer 1

Answer:

Chair  x₁ = 10

Sofa   x₂ = 18

z(max)  = 2250 $

Step-by-step explanation:

Information:

Operation-Profit             Carpentry         Finishing      Upholstery     Profit

                                           hours                 hours              hours             $

Chair (x₁)                                3                        9                      2                90

Sofa  (x₂)                                 2                        4                     10               75

Objective Function z:

z =  90*x₁ + 75*x₂

Constrains:

1.-66 hours of carpentry available

3*x₁ + 2*x₂ ≤ 66

2.- 180  hours of finishing available

9*x₁  +  4*x₂ ≤  180

3.- 200 hours of upholstery

2*x₁  +  10*x₂  ≤ 200

Model:

z = 90*x₁ + 75*x₂    to maximize

Subject to:

3*x₁ + 2*x₂ ≤ 66

9*x₁  +  4*x₂ ≤  180

2*x₁  + 10*x₂  ≤ 200

x₁ >= 0  x₂ >= 0

From simplex method solver we get the answer

x₁ = 10         x₂  = 18       z = 2250

Answer 2

The linear programming model is:

Maximize [tex]\mathbf{Z = 90x + 75y}[/tex]Subject to [tex]\mathbf{3x + 2y \le 66}[/tex], [tex]\mathbf{9x + 4y \le 180}[/tex], [tex]\mathbf{2x + 10y \le 200}[/tex], [tex]\mathbf{x,y \ge 0}[/tex]

Represent sofa with y and chairs with x.

The given parameters are:

Carpentry:

[tex]\mathbf{Chair =3\ hours}[/tex]

[tex]\mathbf{Sofa =2\ hours}[/tex]

[tex]\mathbf{Available = 66\ hours}[/tex]

So, we have:

[tex]\mathbf{3x + 2y \le 66}[/tex]

Finishing

[tex]\mathbf{Chair =9\ hours}[/tex]

[tex]\mathbf{Sofa =4\ hours}[/tex]

[tex]\mathbf{Available = 180\ hours}[/tex]

So, we have:

[tex]\mathbf{9x + 4y \le 180}[/tex]

Upholstery

[tex]\mathbf{Chair =2\ hours}[/tex]

[tex]\mathbf{Sofa =10\ hours}[/tex]

[tex]\mathbf{Available = 200\ hours}[/tex]

So, we have:

[tex]\mathbf{2x + 10y \le 200}[/tex]

The profit is given as: $90 per chair, and $75 per sofa.

So, the objective function is:

[tex]\mathbf{Z = 90x + 75y}[/tex]

Hence, the linear programming model is:

Maximize [tex]\mathbf{Z = 90x + 75y}[/tex]

Subject to

[tex]\mathbf{3x + 2y \le 66}[/tex]

[tex]\mathbf{9x + 4y \le 180}[/tex]

[tex]\mathbf{2x + 10y \le 200}[/tex]

[tex]\mathbf{x,y \ge 0}[/tex]

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Related Questions



A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior
citizens. Create a function f (x) which models the amount, in dollars, a senior citizen would pay for 2 pounds
of bananas on Wednesday

Answers

Answer:

2

Step-by-step explanation:

f(x)= 0.90(0.59*2)

A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior citizens. We need to create a function f(x) which models the amount in dollars, a senior citizen would pay for 2 pounds

What is a simple Equation?

A mathematical equation which represents the relationship of two expressions on either side of the sign.

The 10% discount will make it so the senior citizens will pay 90% of the price.

90%=0.90

Also we need to know that 0.59*2 means how much money per pound the bananas cost.

So when you put it together, you should get f(x)=0.90(0.59*2)

The function f (x)=0.90(0.59*2) which models the amount, in dollars, a senior citizen would pay for 2 pounds of bananas on Wednesday

So the required function is f(x)=0.90(0.59*2)

To learn more on simple equations click here:https://brainly.com/question/19459372

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Which expression is equivalent to (65) (62)?
о
610
615

Answers

Answer: 615

Step-by-step explanation:

Uma caixa contém 40 bolinhas de jogo de tênis, sendo 10 verde, 14 azuis e 16 vermelhas. Retirando uma bola ao acaso da caixa, qual a probabilidade desta bola ser vermelha? Assinale a alternativa correta, que representa a probabilidade desta situação.
qual dessas quatro e a resposta .
14 / 40
15 / 40
16 / 40
17 / 40

Answers

Answer:

p = 15/40

Step-by-step explanation:

Since the total number of marbles is 40, that is our size of the sample. there are 16 red ones on that sample, so the probability of extracting a red marble from the box is given by the ratio of successes divided the total number of marbles:

p = 15/40

Pls help - Solve for x​

Answers

Answer:

-3

3x/(x^2+6x) = 1 is this the qstn?

if so then the ans is -3


The population of New Town is increasing by 6% a year.
If the population was 19613 on January 1st, 2000, what was it on January 1st, 2020?
Give your answer to the nearest 100 people.

Answers

Answer:

After population (A) = 62,902 (Approx)

Step-by-step explanation:

Given:

Current population (P) = 19613

Number of years (n) = 2020 - 2000 = 20 year

Rate of growth (r) = 6% = 0.06

Find:

After population (A)

Computation:

[tex]After\ population (A) = Current\ population (P)[1+r]^n \\\\After\ population (A) = 19613[1+0.06]^{20} \\\\After\ population (A) = 19613[1.06]^{20} \\\\After\ population (A) = 62,901.548[/tex]

1 5/16 divided by 7/12

Answers

2.25 this is the correct answer

How can a transformed quadratic equation be used real life situation?​

Answers

Answer:

Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.

Step-by-step explanation:

7(10x+5-9x)=70
I rly need help on this

Answers

Answer:

x = 5

Step-by-step explanation:

1. Combine like terms

2. Multiply by 1

3. Distribute

4. Subtract  3

5  from both sides of the equation

5. Simplify

6. Divide both sides of the equation by the same term

7. Simplify

Answer: x=5

Step by Step Explanation:
7(10x+5-9x)=70 distributive property
70x+35-63x=70 subtract common terms
7x+35=70 subtract both sides by 35
7x=35 divide both sides by 7
x=5


Robert bought a 6 pack of cans of iced tea for $2.70. About how much is the unit cost for each can of iced tea?

Answers

Answer:

.45$

Step-by-step explanation:

2.70 ÷ 6

Answer:

$0.45

Step-by-step explanation:

If 6 cans of iced tea costs $2.70,

1 can would cost ($2.70 ÷ 6)

A 40 ​-inch board is to be cut into three pieces so that the second piece is 4 as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first​ piece, find the lengths of all three pieces.

Answers

Answer:

4*4=16 INCHES FOR THE SECOND PIECE. 5*4=20 INCHES FOR THE LONGEST PIECE.

Step-by-step explanation:

x = 20 inch, the length of the first piece

What is mathematical expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

given,

Total length = 40 inch

let first piece be = x inch

second piece = 4 times of first piece = 4x inch

third piece = 5 times of first piece = 5x inch

So,

x + 4x + 5x = 200

10x = 200

x = 200/10

x = 20

Therefore, the length of the first piece is 20 inch

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Plz help
6y+2(y+1)

Distributive Property and Fractions

Answers

6y^2 + 6y + 2y + 2 = 6y^2 + 8y + 2

The way you do this is basically multiplying the values in the brackets with 6y, and then adding that to the same values multiplied by 2.

Two divers are swimming at different depths below sea level. One diver is at -25.5 ft. The other diver is at -40.75 ft. How far are the divers from each other?

Answers

Answer:

66.25 ft

Step-by-step explanation:

25.5 + 40.75

66.25

They are 66.25 feet away from each other.

Please let me know if I'm wrong!

Choose all sets that contain the number - 2.22.

Natural numbers

whole numbers

integers

Rational numbers

irrational numbers

Real numbers​

Answers

Rational numbers? And integers?

Answer:

D, F

Step-by-step explanation:

rational numbers

real numbers

Multiply 3/5 by 10/21 Express your answer in simplest form ​

Answers

Answer:

2/7

Step-by-step explanation:

Answer:

3/5 * 10/21= 2/7

please i need in under 20 mintute quick

Answers

Answer:

its been over twenty minutes. did you figure it out ?

What do you know about the slope of two parallel lines? *
They have the opposite sign of each other
They are reciprocals of each other
They have the same slope
They have negative reciprocal slopes

Answers

Answer:

same slope

Step-by-step explanation:

if it has the same slope then the you will know the two lines are parallel

hope this helps

brainliest?

Alan Jeff and Lucy all take their pets to the same vet. The pets are a dog a cat and a rabbit. The names of the pets are Blackie bandit and Moe. Read the clues to determine the kind of pet each owner has and the name of the pet. Mark the correct boxes on the grid to show your answers.

Answers

Answer:

i need at least a pick of the problom

Step-by-step explanation:

Answer:

huh?

Step-by-step explanation:

How much mixed spice will she need for 6 spice

Answers

Answer:

who

Step-by-step explanation:

There are 20 students in a class and 70% of these students passed their Biology test.
What number of these students passed their test? Round your answer to the nearest whole
number if necessary.

Answers

Answer:

The answer is 14 students.

Step-by-step explanation:

70% of 20 = 14

Two shooters, Rodney and Philip, practice at a shooting range. They fire 100 rounds each at separate targets. The targets are marked with circles and each bullet hitting a particular circle gets them a particular number of points. 60 rounds are selected at random. The sample mean scores of Rodney and Philip are 8 and 10, respectively. And, their variances are 0.25 and 0.50, respectively The standard error of the difference between their mean scores is ______________ (Round your answer to two decimal places.) The 95% confidence interval for the difference between the mean scores Rodney and Philip is ________ _____________: (Enter a minus sign if your answer is negative. Round your answer to two decimal places.)

Answers

Answer:

A) SE = 0.1118

B) 95% Confidence interval is;

-2.22 < μ1 - μ2 < -1.78

Step-by-step explanation:

We are given;

Sample size; n = 60

Sample mean 1; x1 = 8

Sample mean 2; x2 = 10

Variance 1; v1 = 0.25

Variance 2; V2 = 0.5

Now,

Standard deviation is given by the formula ;

σ = √variance

Thus;

σ1 = √0.25

σ1 = 0.5

σ2 = √0.5

σ2 = 0.7071

Formula for standard error of mean is;

SE = σ/√n

Thus;

SE1 = 0.5/√60

SE1 = 0.06455

SE2 = 0.7071/√60

SE2 = 0.0913

The standard error of the difference between their mean scores would be;

SE = √[(SE1)² + (SE2)²]

SE = √(0.06455² + 0.0913²)

SE = 0.1118

Formula for 95% confidence interval is;

(x1 - x2) - ((Z_α/2) × SE) < μ1 - μ2 < (x1 - x2) + ((Z_α/2) × SE)

Where Z_α/2 is the critical value. At confidence interval of 95%, we have a critical value of 1.96 from tables.

Thus, plugging in the relevant values, we have;

(8 - 10) - (1.96 × 0.1118) < μ1 - μ2 < (8 - 10) + (1.96 × 0.1118)

-2.22 < μ1 - μ2 < -1.78

4 1/8÷2 3/4 convert the mixed numbers to improper fractions​

Answers

Answer:

Check picture

Step-by-step explanation:

9514 1404 393

Answer:

  1 1/2

Step-by-step explanation:

  [tex]\dfrac{4\dfrac{1}{8}}{2\dfrac{3}{4}}=\dfrac{\left(\dfrac{4\cdot8+1}{8}\right)}{\left(\dfrac{2\cdot4+3}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{11}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{22}{8}\right)}=\dfrac{33}{22}=\dfrac{3}{2}[/tex]

Then the improper fraction 3/2 can be written as the mixed number 1 1/2.

  (4 1/8) / (2 3/4) = 1 1/2

_____

Comment on division of fractions

Fractions can be divided several ways. Two ways that are commonly taught are "invert and multiply", or "match denominators". Here, we have used the second of these methods.

If we were to "invert and multiply", the computation would be ...

  (33/8)(4/11) = (33/11)(4/8) = 3(1/2) = 3/2

Instead, we multiplied 11/4 by 2/2 to make it be 22/8, so having a denominator of 8 matching that of the numerator. Then the value of the compound fraction is the ratio of the numerators:

  (33/8)/(22/8) = 33/22 = (3/2)(11/11) = 3/2

sixteen people wore white socks. The ratio of those who wore white socks to those who wore black socks 1:2. How many people wore black socks?

Answers

Answer:

It should be 32.

Step-by-step explanation:

Evaluate each expression for s=4 and t=8
1) (25)^2t
2) 2st^2-5^2
3) 2s^2-t^3/16

Answers

Answer:

1. 2.328×[tex]10^{22}[/tex]

2. 487

3. 30.52  OR  0 (see explanation↓)

Step-by-step explanation:

1.[tex](25)^{2t}[/tex]

(sub for t=8)

=[tex]25^{2*8}[/tex]

=[tex]25^{16}[/tex]

=2.328×[tex]10^{22}[/tex]

2.[tex]2st^{2} -5^{2}[/tex]

(sub for s=4 and t=8)

=2×4×[tex]8^{2}[/tex]-[tex]5^{2}[/tex]

=512-25

=487

3.[tex]2s^{2} -t^{3/16}[/tex] (the equation is not clear so I will do [tex]2s^{2} -\frac{t^{3} }{16}[/tex] as well)

FOR [tex]2s^{2} -t^{3/16}[/tex]

(sub s=4 and t=8)

=2×[tex]4^{2}[/tex]-[tex]8^{3/16}[/tex]

=32-1.476826146

=30.52 (to the nearest 2 decimal place)

FOR [tex]2s^{2} -\frac{t^{3} }{16}[/tex]

(sub s=4 and t=8)

=2×[tex]4^{2}[/tex]-[tex]\frac{8^{3} }{16}[/tex]

=32-32

=0

Rewrite the following using the GCF and the distributive property
:32 + 54

Answers

Answer:

GCF: 2

Step-by-step explanation:

GCF: 2

(2*16) + (2*27)

t> -5
can someone show step by step how to solve this equation?

Answers

Answer: The equation cannot be simplified any further.

Explanation: The variable(t) is greater than any number than negative five.

Plz mark brainliest:)

this is the last question i need help on! i will mark brainlessttt :)thanks

Answers

Answer:

A.3

Step-by-step explanation:

Since the lines are parallel that angle is 90 same as the other. So you plug in all your answers to see with one gives you 90 that being 3 because 30(3)=90.

A proposed change in income tax suggests charging 20% on a person's income up to $30,000 and then 40% on any
income above that. If a person has an income of $47,000, what will be their income tax under the proposal?
Give your answer in dollars to the nearest dollar. Do not include commas or the dollar symbol in your answer.
Provide your answer below

Answers

Answer:

If you get tax you should know the details of the what the tax is FOR

Step-by-step explanation:

Not enough details in question

Answer:

Step-by-step explanation:

Since the person earns over $30,000, they will be charged 20% on $30,000 plus 40% on ($47,000−$30,000)=$17,000. Hence the total amount of tax that they'd need to pay under the proposal is

Total Income Tax=$30,000×20%+$17,000×40%=$30,000×20100+$17,000×40100=$6,000+$6,800=$12,800.

Hewwo! can anyone answer this? giving brainliest to whoever explains! tysm c:

Answers

Answer:

4

Step-by-step explanation:

Basically it's dividing the pounds of dog food to the bags of food by 4

A rectangle has a length of 2x+1 and a width of 3x-2.
Write an expression for the area of the rectangle.​

Answers

Answer:

(2x+1)x(3x-2)

Step-by-step explanation:

area  of rectangle = length * width

length = 2x+1

width = 3x-2

area = (2x+1) x (3x-2)

If f(x) = 2x2 + x-1, then f(-5)
= ?

Answers

Answer:

-54

Step-by-step explanation:

(-5)^2 = -25

2(-25)+ -5 +1 =-54

Answer:

f(-5) = -2

Step-by-step explanation:

f(-5) = 2x2 + -5 -1

f(-5) = 4 - 6

f(-5) = -2

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