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

4 sinA + 5 sinA what is the answer of it​

Answers

Answer:

9 sinA

Step-by-step explanation:

Adding them is all you can do to simplify.

Phil Dunphy, a real estate agent, is considering whether he should list an unusual $262,023 house for sale. If he lists it, he will need to spend $3,111 in advertising, staging, and fresh cookies. The current owner has given Phil 6 months to sell the house. If he sells it, he will receive a commission of $19,752. If he is unable to sell the house, he will lose the listing and his expenses. Phil estimates the probability of selling this house in 6 months to be 40%. What is the expected profit on this listing?

Answers

Answer: $4,789.80

Step-by-step explanation:

If Phil is able to sell the house, the profit he makes will be;

= Commission - expenses

= 19,752 - 3,111

= $16,641

If he is unable to sell in 6 months he will lose $3,111.

His expected profit will be a weighted average of the two possibilities;

= (40% * 16,641) + ( 60% * -3,111)

= ‭6,656.4‬0 + (-‭1,866.6‬)

= $4,789.80

Find the value of x and measure of ∠3
∠3=2x+7
∠6=6x+21

Answers

Answer:

the answer is four

Step-by-step explanation:

How much is one pound of oranges according the the chart?

Answers

Answer:

The retail price for bananas and seedless grapes has had a somewhat rockier track record over the past 25 years. Starting at 45 U.S. cents in 1995, the price of bananas per pound reached its peak in 2008, with 62 cents. In 2019, bananas cost consumers an average of 57 U.S. cents per pound. In recent years, the retail price of seedless Thompson grapes had decreased: the price stood at roughly 3 U.S. dollars per pound in 2014 and dropped to approximately 2.40 U.S. dollars in 2019.

Sales growth of fresh fruit

In 2019, sales numbers for papayas increased by roughly 15 percent in the United States, making it the type of fresh fruit that experienced the highest rate of sales growth that year. Kiwis, berries, and limes were some of the other fruit types that experienced growth in the United States, while sales percentages for apricots, oranges, and tangelos decreased considerably

Step-by-step explanation:

Answer:

1.50

Step-by-step explanation:

On the X-axis where oranges are graphed, you run until you get to 1 pound. Then you go up from the X-axis and see where it connects with the Y-axis (total cost)

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:

Write an equation of the line passing through point P(−2, 6) that is parallel to the line x=−5.

Answers

Answer:

x = -2

Step-by-step explanation:

The line x = - 5 means it is a straight vertical line that has no slope. This means that the slope is undefined.

Now, for this line to be parallel to the line passing through point P(−2, 6), it means the line will be a vertical line too with the equation of form (x = a).

Thus, the equation of the line is x = -2

The equation of the line is given by:

[tex]x = -2[/tex]

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which:

m is the slope, which is the rate of change.b is the y-intercept, which is the value of x when y = 0.If two lines are parallel, they have the same slope.

Line x = -5 is a horizontal line, thus, it's slope is undefined.

A line parallel will also be horizontal, with undefined slope.

It passes through point P(-2,6), thus, the equation of the line is:

[tex]x = -2[/tex]

A similar problem is given at https://brainly.com/question/16302622

How do you do this question?

Answers

Answer:

Diverges

Step-by-step explanation:

an = 7 / n^(1 + 1/n)

As n approaches infinity, an approaches 7 / n.

bn = 7 / n

Apply Limit Comparison Test.

lim(n→∞) an / bn

= lim(n→∞) [7 / n^(1 + 1/n)] / (7 / n)

= lim(n→∞) n / n^(1 + 1/n)

= lim(n→∞) 1 / n^(1/n)

= lim(n→∞) 1 / n⁰

= 1

The limit is greater than 0, and bn diverges, so an also diverges.

The bowling lanes charge an hourly fee for bowling and $2 to rent shoes for the day. Gerry rented shoes and bowled for 2 hours and was charged $12
Which equation represents the cost, f(x), of bowling as a function of x, the number of hours of bowling?
O f(x) = 4x + 3
Of(x) = 2x + 2
Of(x) = 5x - 2
Of(x) = 5x + 2

Answers

Answer:

d) f(x) = 5x + 2

Step-by-step explanation:

First we need to identify the variables and how they fit into the equation. in this case we know that the equation is f(x) = mx + b where f(x) is the total cost, m is the hourly cost, x is the number of hours bowled, and b is the price of the shoes.

Now, we need to solve for the hourly cost, so to do this we plug in all the known information to get 12 = m(2) + 2

To solve we need to isolate the variable by first subtracting 2 on both sides to get 10 = m(2) and then dividing both sides by 2 to get 5 = m.

Finally, since we now know that the hourly cost is $5 we can plug this information back into the equation to get f(x) = 5x + 2

Carmine paid an electrician x dollars per hour for a 5-hour job plus $70 for parts. The total charge was $320. Which equation can be used to determine how much the electrician charged per hour? (Tek 7.10A)

Answers

Answer:

First one (5x=320-70)

Step-by-step explanation:

If she paid 70$ for parts, then you have to subtract it from 320$ because that is the total. Therefore, 5x will be equal to 320-70 or 5x=320-70 :)

identify the first term of the algebraic expression. Indicate whether the term is a variable or a constant term.
5y + 8b

Answers

Answer:

Someone text me on sc queenalyssa_05

Step-by-step explanation:

Answer:5

Step-by-step explanation:

Find all the zeros of f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12

Answers

Answer:

x=-2  x=2  x = 1/2   x=3

Step-by-step explanation:

f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12

Graph

We see that there is a zero at -2

Using synthetic division

-2      2   -5  -5   20  -12

             -4   18   -26  12

     ------------------------------  

         2   -9  13  -6     0

This gives us ( x+2) ( 2x^3 -9x^2 +13x -6)

We see that there is a zero at 2

Using synthetic division  ( 2x^3 -9x^2 +13x -6)

2       2   -9  13  -6

              4   -10  6

     ------------------------------  

         2   -5  3  0

This gives us ( x+2)   ( x-2) ( 2x^2 -5x+3)

We can factor  ( 2x^2 -5x+3)

( x+2)   ( x-2)  ( 2x -1) ( x-3)

Using the zero product property

( x+2)=0   ( x-2)=0  ( 2x -1)=0 ( x-3)=0

x=-2  x=2  x = 1/2   x=3

How do you show that an inequality is true on a number line?​

Answers

Does it have the open and closed dot?

Part B
Complete the table for the clementines in units of pounds and cost.
В І о
Font Sizes
А
А -
Pounds Cost
II
O

Answers

Answer:

Pounds     Cost

3               $5

6               $10

9               $15

Step-by-step explanation:

I just did this one, and this was the answer.

The system shown below is
.
3x – 4y = 12
6x – 8y = 21

Answers

Answer:

inconsistent

Step-by-step explanation:

Answer:

inconsent

Step-by-step explanation:

Solve the equation 3 + x/-2 =10

Answers

3+x/-2 =10

x/-2 = 10-3

x/-2 = 7

x = 7*-2

x = -14

Answer:

x= -14

Step-by-step explanation:

Jamie borrowed $361.75 from his uncle,
who has agreed to charge him a monthly
simple interest rate of 2.5%. Jamie pays
his uncle back in 7 months.

Answers

Answer:

Jamie will pay back a total of 370.79

Step-by-step explanation:

361.75 x 1.025

Simple interest is not compounded so just multiply the borrowed amount by

1 + .025

He pays 370.28125.

What is Simple Interest?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given:

Jamie borrowed =  $361.75

Simple interest = 2.5%

As, Simple interest is not compounded.

so,

361.75 x 1.025

=370.28125

Hence, he pays 370.28125.

Learn more about simple interest here:

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#SPJ2

The annual fundraising goal of a sports team is​ $100,000. So far ​$41,317 has been raised. How much more money is needed to reach the​ goal?​

Answers

Answer:

58,683

Step-by-step explanation:

subtract

3.A normal bus carries x passengers.
A large bus will carry twice as many passengers than the normal bus
A small bus will carry 8 passengers less than the normal bus.
Altogether the buses carry 128 passengers.
(a) Form a simplified equation in terms of x

Answers

Answer:  A)    4x -8 = 128  

Step-by-step explanation:

We will represent the amount that the normal bus carries by   n= x  

We will represent  the amount that the large bus carries by  l = 2x  

We will also represent the amount that the small bus carries by  s = x-8  

Now add them to equal to 128.

x + 2x + x -8 = 128    

    4x -8 = 128  

Evaluate the following question:f(x) = 3x - 7 for f(10)

Answers

Answer:

f(10) = 23

Step-by-step explanation:

you plug in 10 for the x in the equation and then solve. So 3 x 10 = 30 then minus 7

Answer:

x=-1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

x=−1

Prove the following statement directly from the definitions. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r

Answers

Answer:

- Integers, b ≠ 0 and d ≠ 0.

- r - s = (ad - bc)/bd.

- products and differences of integers are integers.

-  zero product property

- quotient.

Step-by-step explanation:

Rational numbers are integers that can take the form of numerator divided by a denominator, that is to say in the form of 'a/b;. So, we are given from the question or problem to prove and fill in the gap the correct information or data:

For the first part of the question:

The missing data in the gap = Integers; b ≠ 0 and d ≠ 0. That is to say the denominators can not be zero or say that the denominators are non zero. This is one of the properties or let us say one of the ways of identifying a Rational number.

For the second part:

The missing data in the gap = a/b - c/d =  (ad - bc)/bd. This is the representation in  a simplified form.

For the third part:

The missing data or information = products and differences of integers are integers.

For the fourth part:

The missing data or information: zero product property, that is to say the product of the numerators is not equal to zero, or it is non zero.

For the fifth part:

The missing data or information: quotient.  r - s is a quotient of two integers.

Coweta Nutrition sells shakes for $3.39 each. They also sell tea for $2.50. If Mrs.
Morgan bought 1 tea and spent $19.45 this week, not including tax, how many
shakes did she buy?*

Answers

Answer:

she bought 5 shakes

Step-by-step explanation:

shakes: $3.39

tea: $2.50

2.50 + 3.39s = 19.45

3.39s = 16.95

s = 16.95 ÷ 3.39

s = 5

Check:

2.50 + 3.39(5) = 19.45

or

2.50 + 3.39 + 3.39 + 3.39 + 3.39 + 3.39 =  19.45

She bought 5 snakes

what is 6 4/9 as a impropor fraction

Answers

6 4/9 as an improper fraction is 58/9

3. ​Subtract 1.7 - 0.8 = _____ tenths - _____ tenths = _____ tenths = ______ what are the tenths

Answers

Answer:

17 tenths - 8 tenths=9 tenths

Step-by-step explanation:

1.7 tenths is 17 tenths, we can see that by multiplying 1.7x10 to get 17

dot he sam with 0.8 to get 8 tenths

ti find the answer, subtract the units. 17-8=9

Pls pls Pls pls Pls Pls help me pls pls pls pls pls pls ASAP pls pls pls Pls pls Pls pls Pls Pls help me pls pls pls pls pls pls ASAP pls pls pls Pls I WILLL BRAINLIEST!!!!

Answers

Answer:

y = -3x - 8

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step 1: Define

slope m = -3

y-intercept = -8

Step 2: Plug into equation

y = -3x - 8


HELP PLEASE BRAINLESS ANSWER GETS 20 POINTS


An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using d for distance in kilometers and t for number of hours, an
equation that represents this situation is d-50t.

Enter the smaller of the two constants of proportionality.

Answers

Answer:

t=8

Step-by-step explanation:

400 divided by 50 hopefully that helps with your question

Can someone please help, ty!! (Will mark brainliest)

Answers

[tex]\large\underline{\bf\red{Solution:-}}[/tex]

Given two points are :-

( -1 , 3)( 0 , -5)

So , we know Two point form into equⁿ using a formula , which is

[tex]\boxed{\purple{\bf{\dag y - y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}}}[/tex]

So, on substituting respective values ,

=> y - 3 = (-5-3)/0-(-1) × ( x - 3)

=> y - 3 = -8/1 ( x - 3)

=> y - 3 = -8x +24

=> 8x + y -27 = 0

5, 6, 7 8,? Plzzzzzzzz

Answers

Answer:

5. perpendicular

6. neither

7. parallel

8. perpendicular.

Step-by-step explanation:

i used the slope formula to compare them. it's easier than graphing if you want to be exactly sure of your answers

The net of a rectangular shipping box is shown.

What is the surface area, in square centimeters, of the box?

Answers

Answer:

It would be 376.

On a cold morning, the temperature at 7AM is -10 degrees F and rises two degrees per hour. What will the temperature be at noon?
Answer:
Equation:
Hours after 7AM (x) 0, 1, 2
Temp in F (y) -10, -8, -6
Use these for your coordinates

Answer the question, provide the equation, fill in the table and create the graph.

Answers

Answer:

it would be 60 degrees at noon

Step-by-step explanation:

I need help !!
Don’t understand it..

Answers

Answer:

d

Step-by-step explanation:

Answer:

B. h(x)=(x+1) (10x-1)

Step-by-step explanation:

B. h(x) = (x+1) (10x-1)

h(x)=10x^2+10x-x-1

h(x)=10x^2+9x-1

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