A furniture company is producing three types of furniture. Product A requires 7 board feet of wood and 4 lbs of wicker. Product B requires 5 board feet of wood and 5 lbs of wicker. Product C requires 4 board feet of wood and 3 lbs of wicker. There are 3000 board feet of wood available for product and 1400 lbs of wicker. Product A earns a profit margin of $35 a unit, Product B earns a profit margin of $42 a unit, and Product C earns a profit margin of $20 a unit. Formulate the problem as a linear program.

Answers

Answer 1

Given:

Product A requires 7 board feet of wood and 4 lbs of wicker.

Product B requires 5 board feet of wood and 5 lbs of wicker.

Product C requires 4 board feet of wood and 3 lbs of wicker.

Available wood = 3000 board feet

Available wicker = 1400 lbs

Profit margin of A = $35 per unit

Profit margin of B = $42 per unit

Profit margin of C = $20 per unit

To find:

The linear programming problem for given situation.

Solution:

Let the number of units produced of products A, B and C are x, y and z respectively.

                                Product A       Product B           Product C      Total

Board feet of wood       7                       5                       4               3000

wicker                            4                       5                        3               1400

Objective function: Maximize [tex]z=35x+42y+20z[/tex]

s.t.,

Board feet of wood  : [tex]7x+5y+4x\leq 3000[/tex]

Wicker : [tex]4x+5y+3x\leq 1400[/tex]

Number of units  cannot be negative. So, [tex]x,y,z\geq 0[/tex].

Therefore, the required LPP is

Maximize [tex]z=35x+42y+20z[/tex]

s.t.,

[tex]7x+5y+4x\leq 3000[/tex]

[tex]4x+5y+3x\leq 1400[/tex]

[tex]x,y,z\geq 0[/tex]


Related Questions

Find the value of the power.
3 exponent 5

Answers

Answer:

243

Step-by-step explanation:

3*3*3*3*3=243

Answer:

243

Step-by-step explanation:

Justin bought 12 souvenirs
during 6 days of vacation. How
many days will Justin have to
spend on vacation before he will
have bought a total of 20
souvenirs ?

Answers

Answer:

10

Step-by-step explanation:

10 days, because he got 2 souvenirs a day, so 20/2 = 10

Determine the ordered pair that satisfies the equation, -5x - 6y = -8.

Answers

Answer:

-2&-4

Step-by-step explanation:

-5x-6y=-8

it is a quadratic equation:

-5x-6y+8=0

(x-2)(x-4)

cross multiple and you'll get

-5x-6y+8=0

I don't know if you want to solve for x or y so I'm gonna do both.

Answer: x=-6/5y+8/5; y=-5/6x+4/3

Explanation: -5x-6y=-8 start by answering for x by adding it to both sides, -6y=-8+5x then add 8 to both sides, -6y+8=5x then divide 5 from both sides x=-6/5y+8/5. Now lets solve for y -5x-6y=-8 add 6y to both sides, -5x=-8+6y then add 8 to both sides, -5x+8=6y, then divide 6 from both sides -5/6x+8/6=y then simplify 8/6 into 4/3 and rewrite the equation y=-5/6x+4/3

Find the standard deviation of the following data. Round your answer to one decimal place. x 00 11 22 33 44 55 P(X

Answers

Complete question :

Find the standard deviation of the following data. Round your answer to one decimal place.

X: 0 1 2 3 4 5

P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2

Answer:

1.833

Step-by-step explanation:

Given the data :

X: 0 1 2 3 4 5

P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2

Standard deviation (s) = Sqrt[Σx²*f(x) - E(x)²]

E(x) = (0*0.2) + (1*0.3)+(2*0.1)+(3*0.1) + (4*0.1) + (5 * 0.2) = 2.2

Sqrt[Σx²*f(x) - E(x)²]: [(0^2 * 0.2)+(1^2 * 0.3)+(2^2 * 0.1)+(3^2 * 0.1) + (4^2 * 0.1) + (5^2 * 0.2)] - 2.2²

Sqrt(8.2 - 4.84) = 1.833

what is the value of the Expression below ​

Answers

Your answer is -2 (aka option b that would be)

In a square, what is the relationship between the length of a side and the area?
A. proportional
B. cannot be determined
c. non proportional
d. ratio

Answers

To find this answer I watched a Video called is side length & area proportional? by Khan Academy this is a very good website I use a lot!
The answer is non proportional I believe because the side length is x, so is the other side lengths because in a desire side lengths are all equal and to find area you do x squared or x times x. So they are not proportional because there will be different numbers for each. Ex. X= 2, area ( x squared ) is 4.

The relationship between the length of a side and the area is non proportional. so option C is correct.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a square, we need to find the relationship between the length of a side and the area.

The answer is non proportional because the side length is x, so is the other side lengths.

The side lengths are all equal and to find area you do x squared or x times x.

So they are not proportional because there will be different numbers for each.

For example. X= 2, area ( x squared ) is 4.

Hence, The relationship between the length of a side and the area is non proportional. so option C is correct.

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ2

Pls I need help ASAP

Answers

Answer:

the answer is 1/8

thank you

if you loved my answer then please like it and mark as brainliest

a stone which is dropped into a dry well hits the bottom in 2.2s how deep is the well. take g=10m/s​

Answers

Answer:

23.7m

Step-by-step explanation:

Given parameters:

       Time taken = 2.2s

     Acceleration due to gravity = 10m/s

Unknown:

Depth of the well  = ?

Solution:

To solve this problem, we simply apply one of the motion equations;

        S = ut + [tex]\frac{1}{2}[/tex] gt²

    where S = depth of the well

                u = initial velocity

                t = time taken

               g = acceleration due to gravity

 Input the parameters and solve for S;

   Note initial velocity = 0;

     S = [tex]\frac{1}{2}[/tex] x 9.8 x 2.2²

    S = 23.7m

Solve for X using Special Rights

Answers

Answer:

c) 10√2

Step-by-step explanation:

Two angles are same, means this is an isosceles triangle.

So,

x=10

Now, by using pythagoras theorem,

y=√(10²+10²)

=10√2

Write the equation of the line that passes through the given points.
(0,5) and (-2,-4)

Answers

Answer:

[tex]y=\frac{9}{2}x+5[/tex]

Step-by-step explanation:

To find the equation of the a line that passes through the two given points, we must first find the slope between the two points. We can do this by using the slope formula. The slope formula is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where m is the slope and (x₁, y₁) and (x₂, y₂) are two points.

By plugging in (-2, -4) and (0, 5) for (x₁, y₁) and (x₂, y₂) respectively, we get:

[tex]y=\frac{5-(-4)}{0-(-2)}=\frac{9}{2}[/tex]

So the slope is 9/2. Now we that we have found the slope, we can write an equation. Normally, when we are given two points, we would pick one of the points and plug it into the point-slope form and then solve for slope-intercept form. Here, notice that one of the points give, (0, 5), is the y-intercept. Knowing this, we can plug in 5 for the y-intercept into the slope-intercept form to get our equation. Remember, slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

Pugging in 9/2 for m and 5 for b we get:

[tex]y=\frac{9}{2}x+5[/tex]

which would be our equation.

I hope this helps. Happy studying.

Carl wrote three numbers between 0.47 and 0.48 What numbers did Carl write?

Answers

Answer:

Three examples are 0.471, 0.472, 0.473.

Always remember there are more than 2 place values in decimals! Do not be afraid to extend it. Have a nice day and mark brainliest if possible :)

A taxi company charges $3 per ride plus $1.50 for each mile traveled. Andrea wants to spend no more than $24 on a taxi ride. How many miles can Andrea travel? Select all that apply.

Answers

Answer:

x=14

Step-by-step explanation:

3+1.50x=24

24-3=21

21/1.50=14

Answer is C which is 14

In a population of 271 Dd parrots, predators kill 55. What is the approximate fitness of the genotype?

Fitness of Dd: 20%
Fitness of Dd: 40%
Fitness of Dd: 60%
Fitness of Dd: 80%

Answers

Answer:

60%

Step-by-step explanation:

They killed quite a bit and a lot were left.

What is the value of x?

sin(x+22)°=cos(2x−7)°

Answers

Answer:

x is 25

Step-by-step explanation:

sin(x+22)° = cos(2x-7)°

since,

sin theta = cos(90 - theta)

we can substitute that in (let theta = x + 22)

sin(x + 22) = cos(90 - (x+22))

we also know

sin(x+22) = cos(2x-7)

thus cos(90 - (x+22)) = cos(2x-7)

cos(90 - (x +22)) = cos(2x-7)

cos(90 - x -22) = cos(2x - 7)

cos(68 - x) = cos(2x - 7)

68 - x = 2x - 7

68 + 7 = 2x + x

75 = 3x

x = 75/3

x = 25

the mass of earth is approximately 5.9×10^24 kg,and the mass of venus is approximately 4.9×10^24 kg. a. find the combined mass b. given that mass of the sun is approximately 1.9 × 10^30 kg how many venues and earths would it take to equal the mass of the sun.​

Answers

a) Combined mass of earth and venues is 10.8 × 10²⁴. b) There are total 18989.2 kg taking earth and venue to equal to the sun.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given that,

Mass of earth = 5.9 × 10²⁴ kg

Mass of venus = 4.9 ×  10²⁴ kg

a) Combined mass of earth and venus

5.9 × 10²⁴ +  4.9 ×  10²⁴ = 10.8 × 10²⁴

b) If the mass of the sun =  1.9 × 10³⁰

Let's say the total gain of earth and venus combined x so it will equal the mass.

Then,

10.8 × 10²⁴ + x = 1.9 × 10³⁰

x = 18989.2 kg

Hence "Combined mass of earth and venues is 10.8 × 10²⁴ and there are a total of 18989.2 kg taking earth and venue to equal to the sun.

To learn more about the arithmetic operators,

brainly.com/question/25834626

#SPJ6

This need help jxb...

Answers

2x, the second answer because the y intercept is 0 and it goes up 2 over 1!!

Answer:

That would be y = 2x.

what are the slopes of the two lines?

Answers

Step-by-step explanation:

The slopes of two lines are equal

Which graph represents a function?

Answers

The third graph represents a function because it passes the vertical line test (VLT). (:

8.032×10^-4 in standard form​

Answers

Answer:

0.0008032

Step-by-step explanation:

Hope this helps!

Answer:

80,320

Step-by-step explanation:

Round 2.1132 to the nearest hundredth.
Answer:

Answers

Answer:

2.11

Step-by-step explanation:

hope this helps :)

Answer:

It would be 2.1100

Step-by-step explanation:

Find the
median
75,75,75,75,90,95,100,100,110,110,136, 136,136,136,180, 180,180
180,180,180

Answers

Answer:

110

Step-by-step explanation:

self explanatory

Find The Difference.
1) 8.5-7.6=
2) 2.5-17.8=
3)-2.9-(7.5)-
4) 3.5-1.9=

Answers

Answer:

0.9

-15.3

-10.4

1.6

Step-by-step explanation:

Let me know if I messed up I think I went to fast

Answer:

1. 0.9

2. -15.3

3. -10.4

4. 1.6

PLEASE HELP ASAP I GIVE YOU BRAINLIEST AND 20 POINTS

can a system of linear equations be inconsistent and dependent? explain.

Answers

Answer:

No

Step-by-step explanation:

Inconsistent means it has no solution, which means they do not intersect

Dependent means it is the same line

You cannot have both the same line and not intersecting.

which number line and expression show how to find the distance from -4 to 1?

Answers

Answer:

the correct answer is C

Can someone please help me I need help and I can’t understand this plsssss

Answers

1a. Multiply a variable by 13, add 2.

1b. Subtract two from both sides, divide both sides by 13. X=3

2a. Subtract 3 from a variable; divide by 5

2a. Multiply both sides by 5,add 3 to each side. x=-2
Solution (1) :

Solution (a) :

step 1. Multiply the variable x with 13 .

step 2. Add 2 to it .

Solution (b) :

Step 1 : Subtract 2 from both sides : 13x + 2 - 2 = 41 - 2 = 39

Step 2 : Divide both the sides by 13 : 13x ÷ 13 = 39 ÷ 13 = 3

x = 3

Solution (2) :

Solution (a) :

Step 1. Subtract 3 from the variable .

Step 2. Divide the result by 5 .

Solution (b) :

[tex]Step \: 1. \: add\: 3 \: to \: both \: the \: sides : \frac{x - 3}{5} + 3 = - 1 + 3

[/tex]

Step 2 : Multiply both the sides by 5 : 5 × 1/5x = 5 × -2/5

x = -2

put 0.12, 0.1225, 3/25, 7/125 in order from least to greatest

Answers

Answer:

Note: 3/25 and 0.12 are the same

0.12, 3/25, 0.056, 0.1225

OR

3/25 0.12, 0.056, 0.01225

Hope this Helps!

how much is twice the size if im 3 ft 7 in tall​

Answers

Answer:

the answer is 7.1 inches tall

i mark as brainliest ​

Answers

Answer:

the third one

Step-by-step explanation:

if im wrong you don't have to mark as braniest

PLEASE HELP !!! Find the missing side lengths

Answers

where is the question?

Snail moves 6 inches in 120 minutes. What was average speed of snail in inches per minute

Answers

Answer:

.2 inches a min.

Step-by-step explanation:

Answer:

0.05

Step-by-step explanation:

6 divided by 120 = 0.05

Hope this helps☺️

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