ME In Andrew's Furniture Shop, he assembles both bookcases and TV stands. Each type of furniture takes him about the same time to assemble. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit. Using the information in the problem, write the constraints. Let a represent number of bookcases, and y represent number of TV stands.

needed: verticies, optimization equation, maxiumum profit and what he needs to sell to achieve that profit.​

Answers

Answer 1

Answer:6 bookcases, 12 TV stands.

Step-by-step explanation:

We can model this using a system of equations. Let b represent how many bookcases he makes, and t how many TV stands he makes. He can make at most 18 pieces, so let's say that b+t <=18. The cost of the bookcases are 20, and the TV stands are 40, so 20b+40t gives us our total cost. We have 600 to spend, so 20b+40t <=600. We want to maximize the equation for profit, which is 60b+100t=P. We have three values we care about, where our inequalities intersect, if we have only TVs, and if we only have bookcases.  But, if b=0 and t=18, then our cost is 720, which is too big. So if we only have tv stands, then we can have at most 15 (40*15=600). So our three cases are: (b=0, t=15), (t=0, b=18), and the intersection, which is where the inequalities are equal. To solve that, b=18-t, 20(18-t)+40t=600, 360-20t+40t=600, 360+20t=600, 20t=240, t=12. b=18-t, b=18-12, b=6. So our final case is (b=6, t=12). Now simply plug those three cases into our equation to maximize, 60*0+15*100=1500. 18*60+0*100=1080. 6*60+12*100=1560. So, our third case yields us the highest profit, and Andrew should make 6 bookcases and 12 TV stands.


Related Questions

6.
Write the equation of a line through points (5, 5) and (1, 0) in point-slope form.

Answers

Answer: \(y=\frac{5}{4} x-\frac{5}{4}\)

The graph shows the distribution of the lengths (in seconds) of videos on a popular video-streaming site. The distribution is approximately Normal, with a mean of 264 seconds and a standard deviation of 75 seconds.

A graph titled Streaming Videos has length (seconds) on the x-axis, going from negative 36 to 564. The highest point of the curve is at 264.

What percentage of videos on the streaming site are between 264 and 489 seconds?

0.15%
49.85%
95%
99.7%

Answers

According to the properties of the standard normal distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Therefore, the answer is 99.7%.

To determine the percentage of videos on the streaming site that are between 264 and 489 seconds, we need to calculate the area under the normal curve within that range. Since the distribution is approximately normal with a mean of 264 seconds and a standard deviation of 75 seconds, we can use the properties of the standard normal distribution to find the desired percentage.

First, we need to convert the values 264 and 489 to z-scores, which represent the number of standard deviations a particular value is away from the mean. The z-score formula is given by:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z1 = (264 - 264) / 75 = 0

z2 = (489 - 264) / 75 = 3

Next, we can use a standard normal distribution table or a calculator to find the area under the curve between z = 0 and z = 3. The area represents the percentage of videos falling within that range. The answer is 99.7% .

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what is the absolute value of -11 2/3

Answers

Answer:

112

Step-by-step explanation:

State the name of the property illustrated.
4(-8+5)= - 32 + 20

Answers

The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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Answer of question 3 pls

Answer of question 3 pls

Answers

The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

What is the shape of the graph of a quadratic function?

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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It takes Colton 14 minutes to decorate 4 cookies. It takes

David 20 minutes to decorate 6 cookies. Who decorates

at a faster rate? Explain how you know

Answers

Answer:

David decorated the cookies at a faster rate than Colton.

Step-by-step explanation:

David decorated one cookie every 3 and 1/3 minutes. Colton decorated one cookie every 3.5 minutes. The way to find the answer to your question is by dividing the number of minutes by the number of cookies decorated.

Help! Quadratic Word Problems!

Help! Quadratic Word Problems!

Answers

Answer:

Step-by-step explanation:

Help! Quadratic Word Problems!

Makayla is a botanist studying production of coconuts by two different groups of her coconut palms. She notices that Group 1 trees produce 25 percent more coconuts than Group 2. based on Makayla's observation, if Group 1 produced 150 coconuts, how many coconuts did group 2 produce?

Answers

If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.

What is proportion?

Proportion refers to the two ratios equated to each other.

Proportion shows how much quantity or value is contained in another.

We depict proportions using fractional values, such as fractions, decimals, and percentages.

The number of coconuts produced by Group 1 trees = 150

The percentage by which Group 1 trees produce more than Group 2 = 25%

Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)

Let Group 2's production = 100% = 150/125 x 100

= 120 coconuts

Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.

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Consider ∠A such that cos A = 12/13.

a) In which quadrant(s) is this angle? Explain.

b) If the sine of the angle is negative, in which quadrant is the angle? Explain.

c) Sketch a diagram to represent the angle in standard position, given that the condition in part b) is true.

d) Find the coordinates of a point on the terminal arm of the angle.

e) Write exact expressions for the other two primary trigonometric ratios for the angle.

Answers

A)

Using the unit circle, for the cos function to be positive, angle A must lie in either quadrant I or quadrant IV

B)

Using the unit circle, If the sine is negative, angle A must lie in either quadrant III or quadrant IV. Since we know that the cosine is positive, this only leaves quadrant IV

D)

cos = adj/hyp

Using Pythagorean theorem,

\(12^{2} +b^{2} = 13^{2}\)

b = ±5 (we know its -5 since we know sinA is negative)

this means that the x coord is 12, and the y coord is -5

any proportion of these two numbers would work as an answer

e.g. (12, -5), (24,-10),  (12/13, -5/13), are all valid answers

E)

sinA = opp/hyp

sinA = -5/13

tanA = opp/adj

tanA = -5/12

how do you write 31.4 in scientific notation?

Answers

Answer:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

3.14

×

10

1

Step-by-step explanation:

Brandon buys a radio for $45.09 in a state where the sales tax is 7%. How much does he pay in taxes? If necessary round to the nearest cent

What is the total Brandon pays for the radio?

Answers

Answer:

Step-by-step explanation:

tax = 7% of $45.09 = 0.07×$45.09 ≅ $3.16

Total cost = $45.09 + $3.16 = $48.25

Which statement is the best definition of an angle

Answers

Answer:

In geometry, an angle can be defined as the figure formed by two rays meeting at a common end point. An angle is represented by the symbol ∠. ... Angles are measured in degrees, using a protractor.

Step-by-step explanation:

hurray

There are 20 books in 4 boxes. How many books are there in 1 box?

Answers

The answer is 5
If you were to take 20 divided by 4 the answer would be 5 books in each box.
Hope this helps :)

Answer:

There are 5 books in 1 box

Step-by-step explanation:

It is quite easy to solve. You have to use division to figure out how many books go in each box. Our division equation will be: 20 ÷ 4 = ?

We will divide 20 by 4 and our answer is 5.

We can double-check our answer by doing multiplication. 5 x 4 = 20, leading us back to the original 20 books that are in boxes.

So, there are 5 books in each box.

Hope this helps! <3

Multiplying rational expressions (16x/4).(20/3x^5)

Answers

Given:

\(\frac{16x}{4}\cdot\frac{20}{3x^5}\)

Required:

To multiply the given rational expression.

Explanation:

Consider the given expression,

\(\frac{16x}{4}\cdot\frac{20}{3x^5}\)

Now

\(\begin{gathered} =\frac{4x}{1}\cdot\frac{20}{3x^5} \\ \\ =4\cdot\frac{20}{3x^4} \\ \\ =\frac{80}{3x^4} \end{gathered}\)

Final Answer:

\(\frac{16x}{4}\frac{20}{3x^{5}}=\frac{80}{3x^4}\)

A skyscraper casts a shadow 200 ft long. If the angle of elevation of the Sun is 38 degrees, then the height of the skyscraper is approximately _____.
A. 200 ft
B. 173.34 ft
D. 156.26 ft

Answers

The height of the skyscraper is D. 156.26 ft

How to determine the value

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

sinecosinetangentcotangentsecantcosecant

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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Violet bakes 7 dozen cookies.
She ate 2 cookies.
She gave 2 dozen cookies to her brother.
She gave 9 cookies to her mother.
How many cookies did Violet have left?
Show your work.

Answers

Answer: 49 cookies

Step-by-step explanation:  7 dozen= 84 , so subtract 84 by the 2 cookies she ate and you'll get 82, now 2 dozen= 24, so now subtract the 24 cookies that she gave to her brother by 82 and you'll get 58, then subtract the nine cookies she gave to her mom by 58 and you'll get 49 cookies.

so basically,, 84-2= 82 -2 = 58 -9= 49

I hope this helped :)

use the given frequency distribution to find the class width, class midpoint, and class boundaries​

use the given frequency distribution to find the class width, class midpoint, and class boundaries

Answers

Based on the table attached, the class boundaries are as follows: 43.5, 49.5, 53.5, 59.5, 63.5, 69.5, 73.5, 79.5.

What is the frequency distribution about?

Temperature (°F) Frequency

40-44 1

45-49 3

50-54 5

55-59 11

60-64 7

65-69 7

70-74 1

A. Viewing at the frequency table, we find that the lower class limits of two consecutive classes are 40 and 44, respectively. Thus the class width is:

 Class width = 44 − 40= 4

B: One can find the class midpoints by putting the average of the lower and upper class limits. So the midpoint of the first class is  seen below:

=  40  - 44 = \(\frac{40 + 44}{2}\)   = 42. In a similar way, we find the rest.

C. The Class boundaries is known to be that which separate the classes removing the class limits. The class boundaries are as follows:

43.5, 49.5, 53.5, 59.5, 63.5, 69.5, 73.5, 79.5

Therefore, Based on the table attached, the class boundaries are as follows: 43.5, 49.5, 53.5, 59.5, 63.5, 69.5, 73.5, 79.5.

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What type of Solution is the product of 2x+1=2x+2

Answers

Answer: no solution

Step-by-step explanation:

Aiden leans a 30-foot ladder against a wall so that it forms an angle of 78^{\circ} ∘ with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.

Answers

Answer:

6.2 approx i believe

Step-by-step explanation:

What are the new coordinates of the figure above if it is dilated by a scale factor of , with the origin as the center of dilation?

Answers

Answer:

could you show a picture and repost thx

Step-by-step explanation:

The picture of milk shown is a prism. The base has an area of 40 cm² and the height of the pitcher is
26 cm. Will the pitcher hold 1 Liter of milk?

The picture of milk shown is a prism. The base has an area of 40 cm and the height of the pitcher is26

Answers

Yes, the pitcher hold 1 Liter of milk.

We have to given that;

The picture of milk is a prism.

And, The base has an area of 40 cm² and the height of the pitcher is 26 cm.

Since, We know that;

Volume of prism is,

V = base area x Height

Now, Substitute all the values, we get;

V = 40 x 26

V = 1040 cm³

Since, 1 liter = 1000 cubic centimeters

Hence, the pitcher hold 1 Liter of milk.

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A sports trophy is in the shape of a cup
30 cm high. The winners are each given
copies of the cup, 7 cm high. One of the
copies holds 100 ml. What is the capacity of the trophy in liters?

Answers

The capacity of the trophy that us 30 cm high is 0.4286 liter

What is an equation?

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

7 cm height cup holds 100 ml. Therefore:

7 cm = 100 ml

For a 30 cm height trophy:

30 cm = 30 cm * 100 ml per 7 cm = 428.57 ml

1000 ml = 1 l

428.57 ml = 428.57 ml * 1 liter per 1000 ml = 0.4286 liter

The capacity of the trophy is 0.4286 liter

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At the supermarket 5 aplples cost $4. What is the cost of 25 apples

Answers

If 5 apples cost $4. How many times do you multiple 5x5 to get 25? The answer would be 5 times.

So 5apples x 5= 25 apples.

4x5=$20.

The answer would be $20

Express the division expression as a fraction in simplest form. Then, rewrite the fraction as a mixed number.
14 ÷ 4 ​

Answers

14/4 is simplified to 7/2 and as a mixed number it would be 3 1/2

Step-by-step explanation:

14 ÷ 4 is the same as the corresponding fraction (because a fraction is nothing else than a mini-division) :

14/4 = 7/2

and 7 divided by 2 is 3 with a remainder of 1. that means 1 time 1/2 remains as fraction.

so, the mixed number is

3 1/2

What is the solution for x in the equation?
-3x+7x-8 = 34+9x-2
OA =
8
OB.
OC. * = -8
OD. = 8
*
118

Answers

Answer:
10

Step-by-step explanation:

-3x+7x-8=34+9x-2

(Combine like terms)

4x-8=32

(Add 8 to each side)

4x=40

(Divide by 4)

X=10

A segment bisector is a line, ray or segment that divides a line segment into two equal parts. in the triangle formed by points A(-1,7), B(1,2), C(7,6) what is the slope of the line that goes through point A and bisects BC?​

Answers

Answer:  -3/5

In decimal form, this is equivalent to -0.6

=================================================

Explanation:

This segment bisector is cutting side BC in half. So we have a point D such that it is between B and C. Also, we can say BD = DC. Refer to the diagram below.

To find the location of D, we'll apply the midpoint formula to points B and C.

B(1,2) and C(7,6) have x coordinates of 1 and 7 respectively. Average those x values to get (1+7)/2 = 8/2 = 4. This is the x coordinate of point D.

Repeat this idea for the y coordinates. We'll get (2+6)/2 = 8/2 = 4 which is the y coordinate of D.

Point D is located at (4,4)

---------------------

The takeaway from that last section, if we were to summarize it in one sentence, is that D is located at (4,4).

Now focus on the points A(-1,7) and D(4,4)

We'll apply the slope formula

m = (y2-y1)/(x2-x1)

m = (4-7)/(4-(-1))

m = (4-7)/(4+1)

m = -3/5 is the slope

Notice that to go from A to D, we can drop down by 3 units and move to the right 5 units. We can say rise = -3 and run = 5; therefore, slope = rise/run = -3/5

A segment bisector is a line, ray or segment that divides a line segment into two equal parts. in the

A piece of art is in the shape of a rectangular pyramid like the figure shown.

A rectangular pyramid with a base of dimensions 7 feet by 6 feet. The two large triangular faces have a height of 7.79 feet. The two small triangular faces have a height of 8 feet.

How much glass is needed to cover the entire pyramid?

Answers

After answering the provided question, we can state that As a result, 145.62 square feet of glass are required to cover the entire pyramid.

what is pyramid?

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The base's edges form triangle faces known as sides that connect to the top.

To determine how much glass is required to cover the entire pyramid, we must first determine the total surface area of the pyramid, including the base.

The formula for calculating the surface area of each triangular face is:

(1/2) x width x height

27.31 square feet = (1/2) x 7 feet x 7.79 feet

24 square feet = (1/2) x 6 feet x 8 feet

Simply multiply the length and width to find the area of the rectangular base:

7 feet by 6 feet equals 42 square feet

As a result, the total surface area of the pyramid is:

145.62 square feet = 2 (27.31 square feet) + 2 (24 square feet) + 42 square feet

As a result, 145.62 square feet of glass are required to cover the entire pyramid.

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Answer: 102.53

Step-by-step explanation:  I calculated all the numbers you gave me and then added them to get 102.53

a train travels forward at 20 m/s. A person on the train stands up and walks towards the back of the train at a velocity of 1 m/s. What is the resultant velocity of the persons motion ?

Answers

The resultant velocity of the person is 19 m/s which is in the opposite direction to the forward motion of the train

Speed of person in forward = 20m/s

Speed of person in backward = 1 m/s

If a person moves in the opposite direction of the train, then the velocity of the person's motion is relative to the ground motion. The difference between the velocity of a person and the velocity of a train is calculated as:

The velocity of the person relative to the ground = Velocity of the train - Velocity of the person's motion

Velocity of person relative to ground = 20 m/s - 1 m/s

The velocity of the person relative to the ground = 19 m/s

Therefore, we can infer that the resultant velocity of the person is 19 m/s.

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Solve x^2+8x+22=0 by completing the square.

Answers

Answer: x = √-6 - 4

Step-by-step explanation:

x^2+8x+22=0

(x+4)^2 - 16 + 22 = 0

(x+4)^2 + 6 = 0

(x+4)^2 = -6

√(x+4)^2 = √-6

x = √-6 - 4            

√6 = 2.449

Help please!
S = 180m
How many strides would a runner take during a 1-hour run (60 min)

Help please!S = 180mHow many strides would a runner take during a 1-hour run (60 min)

Answers

The number of strides the runner will make during 1 hour run will be =

10,800.

How to calculate the total number of strides made by the runner in a hour?

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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For example, the following client code: ComplexShape o = new ComplexShape(); o.addShape(new Circle(3)); o.addShape(new Circle(5)); ComplexShape o1 = new ComplexShape();01.addShape(o); 01.addShape(new Rectangle(4,8)); 01.draw(); builds a (complex) shape consisting of: a complex shape consisting of a circle of radius 3, a circle of radius 5 a rectangle of sides (3,5) Your task in this question is to finish the code for ComplexShape (add any instance variables you need) class ComplexShape implements Shape { public void addShape(Shape s) { } public void draw(Color c) { } } ##I need to change this to allow for more than one space. For example, I type "n nanometer". I get output: 2 n's. Which is great. If i type "n nanometer not included" I get a ValueError: too many values to unpack (expected 2). I need this to accept multiple words with spaces in between. 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Which reactant (X) is missing from the equation shown?X+ PO4 H3PO4 BRAINLIEST QUESTION ON PIC THANK YOU! ultraconservative militia groups, usually secretive, well-armed, and anti-government, are seen to be on the rise in the united states. these groups a good example of List three things that you already know about WWII. What happens to earths surface when horizontal pressure is applied to rocks? (site 1) what is one way in which urban areas in developing nations differ from urban areas in highly developed nations? group of answer choices Elon sent a chain letter to his friends, asking them to forward the letter to more friends. The relationship between the elapsed time, ttt, in days, since Elon sent the email, and the total number of people who receive the email, P(t)P(t)P, left parenthesis, t, right parenthesis, is modeled by the following function: P(t)=43t Complete the following sentence about the daily rate of change in the number of people who receive the email The diagram shows a tennis ball being thrown vertically into the air. When the ball just left the players hand it is at the speed of 5.0 m/s . The tenis ball has the mass of 0.058 kg. Write down the equation that links kinetic energy to mass and speed Is this boxed word a subject or a verb?A savings accounts (earns) interest on your money.A.Subject B.Verb Conjugate the verbs in the following sentences. Remember, the subjunctive is needed in the second clause only. You will use present indicative in the first clause.Part A:Mi madre 1) ___ (insistir) en que yo 2) ___ (estudiar) todos los das y que 3) ___ (participar) en todas mis clases. Mi padre me 4) ___ (aconsejar) que no 5) ___ (ver) mucha televisin y que 6) ___ (ser) una persona honesta.Part B:Paula y yo 1) ___ (querer) que Carlos y Marta 2) ___ (traer) vino a nuestra fiesta y que Jos 3) ___ (preparar) unos entremeses (appetizers). Nuestros amigos nos 4) ___ (recomendar) que 5) ___ (limpiar) nuestra casa y que 6) ___ (hacer) mucha comida antes de la fiesta. Who is Maharana Swarup Singh and why did he support the British?Please give me an answer please i really need it you will be marked brainliest!