Mathematics Middle School

In Andrew’s Furniture Shop, he builds bookshelves and tables. Each type of furniture takes him about the same time to make. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookshelf cost him $20.00 and the materials for each table cost him $45.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table. How many of each piece of furniture should Andrew make to maximize profit?

Answers

Answer 1

Andrew should determine the number of bookshelves and tables to make by using linear programming to solve for the variables given the constraints of his time, material costs, and profits. The optimal solution lies where the constraints intersect within the feasible region.

The student inquired about how many bookshelves and tables Andrew should make in order to maximize profit, given the constraints of time, material cost, and the profit from each item sold. This is a typical problem that can be solved using linear programming, a method in mathematics to achieve the best outcome given a series of linear constraints.

First, let us define two variables: x for the number of bookshelves and y for the number of tables. The constraints given by Andrew's situation are:

x + y \<= 18 (time constraint to make the furniture)

20x + 45y \<= 600 (cost constraint for materials)

Profit function to maximize: P = 60x + 100y

To maximize the profit P, we need to solve for x and y within the given constraints. After setting up the equations, we can graph the constraints and find the feasible region. The solution will be at a vertex of the feasible region, given by the intersection of the constraints. Andrew can use methods like the graphical method, the simplex method, or an algebraic method to find the optimal numbers of bookshelves (x) and tables (y) to maximize his profit.

Related Questions

How many times does 6 go into 22

Answers

Your Answer Is...

3.

Why?

6 X 3 = 18.

Glad I Could Help, And Good Luck!

My Brainly Name: AnonymousGiantsFan
Hey!

We can use long division to solve this,
Let's write it.
[tex]6\overline{|\smallspace22}\space\space\space\space[/tex]
Then, divide [tex]22[/tex] by [tex]6[/tex] to get [tex]3[/tex].
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Multiply the quotient by the divisor...
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace8}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Subtract [tex]18[/tex] from [tex]22[/tex].
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace8}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\space\space\emptyspace4\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
As you can see, our answer using long division would be 3 with a remainder of 4. 

Thanks!
-TetraFish

What is 2.33 written as a mixed number in simplest form?

Answers

2.33.......ok, 2 is ur whole number....33 is ur fraction...the last digit is in the hundredths place....so put it over 100

ur mixed number is 2 33/100...and this does not reduce
233/100..this is already is a simpler form

A juice company did a survey among 100 customers to find their juice preferences. The customers were asked about their preferences for apple or orange juices. Out of the total 35 people who liked apple juice, eight liked orange juice also. There were 20 people who liked orange juice. Part A: Summarize the data by writing the values that the alphabets A to I in the table below represent. (5 points) Like apple juice Do not like apple juice Total Like orange juice A B C Do not like orange juice D E F Total G H I Part B: What percentage of the total people did not like either apple or orange juice? (3 points) Part C: Do the people surveyed have more dislike for apple juice than orange juice? Justify your answer. (2 points)A juice company did a survey among 100 customers to find their juice preferences. The customers were asked about their preferences for apple or orange juices. Out of the total 35 people who liked apple juice, eight liked orange juice also. There were 20 people who liked orange juice. Part A: Summarize the data by writing the values that the alphabets A to I in the table below represent. (5 points) Like apple juice Do not like apple juice Total Like orange juice A B C Do not like orange juice D E F Total G H I Part B: What percentage of the total people did not like either apple or orange juice? (3 points) Part C: Do the people surveyed have more dislike for apple juice than orange juice? Justify your answer. (2 points)

Answers

Seeming how it's just text and I can't determine what part A is talking about I'll make a new table.

Part A:(This table is a three by three table, with the first top two sections being liked apple juice and didn't like apple juice, and the first left two sections being liked orange juice and didn't like orange juice. The end sections are totals.)


         AJ   No  TotalOJ    8     20   28
No    27   45   72
Total 35   55   100

Part B:(What percentage of the total people did not like either apple or orange juice?)

25 people did not like either apple or orange juice so 25/100 is 25%.

Part C:(Do the people surveyed have more dislike for apple juice than orange juice? Justify your answer.)

There were a total of 28 people that liked orange juice against a total of 35 people that liked apple juice, so it is safe to say that out of the 100 surveyed there was more dislike for orange juice than apple juice.

Answer:

Part A: A = 8

B = 20

C = 28

D = 35  

E = 37

F = 72

G = 43

H = 57

I = 200

Part B: 18.5%

Part C:

D = People who do not like Orange Juice

B = People who do not like Apple Juice

I use the values of B and D because these are the values that represent dislike for that juice, and also because adding them together creates a value for not liking either juice.

D = 35

B = 20

So there is a greater dislike for Orange Juice.

Step-by-step explanation:

answer both questions to get brain ( if u cant see all the answers its fine all u need is the question)

Answers

Answer:

a and c

Step-by-step explanation:

1/5 [4(x+2)-(3-x)]=4

Answers

3
Hope you wanted this answer ^.^  

The lines y = 2x + 1 and y = -5x - 6 intersect at?

Answers

They will intersect at (-1, 1)
2x+1=-5x-6    x=-1   put x into equation  for example  y=2*(-1)   y=-2   
so intersect at (-1,-2)

The price of an item has been reduced by 80%. The original price was $45. What is the price of the item now?

Answers

%change=100(final-initial)/initial, so we can say:

100(final-45)/45=-80  multiply both sides by 45

100(final-45)=-3600  divide both sides by 100

final-45=-36  add 45 to both sides

final=9

So the price of the item now is $9.

The number 6√3 is between what two integers and is closer to which integer on the number line.

Between 6 & 7 & is closer to 6
Between 10 & 11 & is closer to 10
Between 6 & 7 & is closer to 7
Between 63 & 64 & is closer to 63

Answers

Between 6&7 is closer to 10

Answer: integer on the number line. Between 6 & 7 & is closer to 6 Between 10 & 11 & is closer to 10 Between 6 & 7 & is closer to 7 Between 63 & 64 & is closer to 63.

Step-by-step explanation:

Is 7/2 the same thing as 3.5

Answers

Yes because 7/2 is 3.5. So you are correct.
yes
3.5 as a fraction is 7/2 but in mixed numbers it's 3 1/2

If the population of Town B is 50% greater than the population of Town A and the populations of Town C is 20% greater than the population of Town A, then what percent greater is the population of Town B tan the population of Town C

Answers

Let
A = population of town A,
B = population of town B,
C = population of town C.

Because the population of town B is 50% greater than that of town A,
B = 1.5A                    (1)

Because the population of town C is 20% greater than that of town A,
C = 1.2A                  (2)

From (1), obtain
A = B/1.5 = (2/3)B        (3)

Substitute (3) into (2).
C = 1.2*(2/3)*B = 0.8B
Divide each side by 0.8.
1.25C = B
This result means that B is 25% greater than C.

Answer: 25%

Which list has the numbers in order from least to greatest

Answers

B is the correct answer.

Twice a number decreased by 15 is equal to -27 . What is the number ?

Answers

2x - 15 = -27
2x = -27 + 15
2x = - 12
x = -12/2
x = -6 <==

classify the following triangle . check all that apply

Answers

One of the angles is more than 90 degrees  ⇒  Obtuse

Two equal sides  ⇒ Isosceles

Answer:

Option (a) and (d) is correct.

The given triangle is obtuse and isosceles.

Step-by-step explanation:

Given : A triangle with measure of one angle is 120° and two legs of the triangle are given equal in length.

We will have to choose the correct classification for the given triangle.

For a triangle if the measure of one the angles is

1) less than 90 then it is acute triangle ,

2) equal to 90 then right triangle

3) greater to 90 then obtuse triangle

Since the measure  of one angle of the triangle is 120° > 90° Thus, the given triangle is obtuse.

For a triangle if all the three sides are equal then it is equilateral triangle, if two sides are equal then it is isosceles and if no side is equal then it is scalene.

Since, for the given triangle, the two legs of the triangle are given equal in length so it is an isosceles triangle.

Thus, the given triangle is obtuse and isosceles.

ANSWER FOR 15 POINTS!!

Which number(s) below belong to the solution set of the inequality? Check all that apply. (Meaning tell me all the ones that apply.)
x + 16 > 51
A. 16
B. 35
C. 80
D. 38
E. 55
F. 34

Answers

The answer is B,C,D and E.
solv

x+16>51
minus 16 both sides
x>35


so any number greater than 35 will work

A doesn't work
B doesn't work
C works
D works
E works
E works
F doesn't work


answers are C,D, E

Which best describes the range of the function f(x) = 2(1/4) after it has been reflected over the y-axis? all real numbers all real numbers less than 0 all real numbers greater than 0 all real numbers less than or equal to 0

Answers

your answer should be C 
all numbers greater than 0

Answer:

All real numbers greater than 0.

Step-by-step explanation:

We have the function, [tex]f(x) = 2(\frac{1}{4})^{x}[/tex].

'Reflection over y-axis means to flip the graph over y-axis', which changes the function by f(x) becomes f(-x).

So, after reflection, the given function transforms into,

[tex]g(x)=f(-x)[/tex]

i.e. [tex]g(x)=2(\frac{1}{4})^{-x}[/tex]

According to the graph of the function g(x), we see that,

Range of [tex]g(x)=2(\frac{1}{4})^{-x}[/tex] is the 'Set of all real non-negative numbers' i.e. {x | x > 0} i.e. [tex](0,\infty)[/tex]

what is the square root of 56x^7

Answers

the value of the square root is 8 because 7 times 8 equals 56
8 is the answer your welcome

A person in the audience of a game show has a 12% chance of winning free movie tickets. What is the chance that a person in the audience does not win free movie tickets? 24% 38% 72% 88%

Answers

It is 88% because 100% - 12% = 88%
the chance of a person not winning a free movie ticket is 88%

is √2/3 a rational or irrational

Answers

sqrt(2/3) = 0.816496

since it is a decimal with no repeating numbers it would be irrational

Irrational because you would get a decimal

What does interior angle A of the polygon in the figure equal? A. 110 B. 150 C. 230 D. 100

Answers

Sum of Interior Angles with n = 6
(n-2) × 180° = 4 x 180 = 720

A = 720 - (50+100-120-110 - 230)
A = 110

answer is A. 110

Which statement is true about the solutions for the equation 3y + 4 = −2?

It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.

Answers

I believe that the answer is B. If y=-2, 3(-2)+4=-2. 3(-2)=-6+4=-2

Answer:

B, One solution

Step-by-step explanation:

Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that 7 cups of water and 3 liters of water filled 9.8 pints. Later, they find that if they start with 5 liters of water and remove 9 cups of water, they end up with 6 pints of water. Model the given two situations as a system of linear equations. Based on your equations, determine the relationship between;

●cups and liters,
●cups and pints,
●and pints and liters.

Show all your work and submit your work along with the resulting relationships.

Answers

7 cups + 3 litres = 9.8 pints 
[tex]7c+3l=9.8p[/tex] ⇒ Equation 1

5 litres - 9 cups = 6 pints
[tex]5l-9c=6p[/tex] ⇒ Equation 2

Relationship between cups and litres
Rearranging equation 1 to make pints the subject
[tex]7c+3l=9.8p[/tex]
[tex]p= \frac{7c+3l}{9.8} [/tex] ⇒ substitute this into Equation 2

[tex]5l-9c= \frac{7c+3l}{9.8} [/tex]
[tex]49l-88.2c=7c+3l[/tex]
[tex]49l-3l=7c+88.2c[/tex]
[tex]46l=95.2c[/tex]
[tex]l=2.1c[/tex]

Hence, 1 litre = 2.1 cups

Relationship between cups and pints
Rearrange equation 1 to make litres the subject
[tex]7c+3l=9.8p[/tex]
[tex]3l=9.8p-7c[/tex]
[tex]l= \frac{9.8p-7c}{3} [/tex] ⇒ Substituting this into Equation 2

[tex]5( \frac{9.8p-7c}{3})-9c=6p [/tex]
[tex] \frac{49p-35c}{3}-9c=6p [/tex]
[tex] \frac{49}{3}p- \frac{35}{3}c-9c=6p [/tex]
[tex] \frac{49p}{3}-6p= \frac{35}{3}+9c [/tex]
[tex] \frac{31}{3}p= \frac{62}{3}c [/tex]
[tex]p=2c[/tex]

Hence, 1 pint = 2 cups

Relationship between pints and litres
Rearranging equation 1 to make cup the subject

[tex]7c=9.8p-3l[/tex]
[tex]c= \frac{9.8p-3l}{7} [/tex] ⇒ subsitute this into equation 2

[tex]5l-9( \frac{9.8p-3l}{7})=6p [/tex]
[tex]5l- \frac{63}{5}p+ \frac{27}{7}l=6p [/tex]
[tex]5l+ \frac{27}{7}l=6p+ \frac{63}{5}p [/tex]
[tex] \frac{62}{7}l= \frac{93}{5}p [/tex]
[tex]l=2.1p[/tex]

Hence, 1 litre = 2.1 pints


Here's work you can copy and paste:

7 cups + 3 liters = 9.8 pints

7c+3l=9.8p

5 liters - 9 cups = 6 pints

5l+9c=6p

Cups and Liters

7c+3l=9.8p

p= 7c+3l/9.8 (put in equation 2)

5l-9c= 7c+3l/9.8

49l-88.2c=7c+3l

49l-3l=7c-88.2c

46l=45.2c

1Liter = 2.1 Cups

Cups and Pints

7c+3l=9.8p

3l=9.8p-7c

l=9.8p-7c/3 (put in equation 2)

5(9.8p-7c/3)-9c=6p

(49p-35c/3)-9c=6p

49/3p-35/3c-9c=6p

49/3p-6p=35/3c+9c

31/3p=62/3c

1 Pint = 2 Cups

Pints and Liters

7c=9.8p-3l

c=9.8p-3l/7 (put in equation 2)

5l-9(9.8p-3l/7)=6p

5l-63/5p+27/7l=6p

5l+27/7l=6p+63/5p

62/7l=93/5p

​1 Liter = 2.1 Pints

the length of a rectangle is 3 centimeters greater than its width the perimeter is 24 cm what are the dimensions of the rectangle

Answers

the width is nine and and the length is 3

If 3a+4b = 4a-4b = 21 find the value of a

Answers

a-4b=4b
a=8b
Plug it in:
24b+4b=21
28b=21
b=21/28
a=8b=6.
Using the 2nd and 3rd you have:

4a-4b=21

4a=21+4b

a=(21+4b)/4

now using 1st and 2nd

3(21+4b)/4+4b=4(21+4b)/4-4b

(63+12b+16b)/4=(84+16b-16b)/4

63+28b=84  

28b=21

b=21/28

b=3/4

.... now using 4a-4b=21 we have

4a-4(3/4)=21

4a=3=21

4a=24

a=6


What is the value of x?

Answers

x+(4x-20)=180
=>5x-20=180
=>5x=200
=>x=40

x/9=4/y=y/36 solve for x

Answers

This is not possible, unless x = 1.

a polynomial of degree zero is constant term. true or false

Answers

The answer is true for a polynomial of degree zero

Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have?

6 ounces
12 ounces
18 ounces
27 ounces

Answers

Answer:

The answer is C. 18 ounces

Step-by-step explanation:


Answer:

c on egde

Step-by-step explanation:

a student scores 71 out of 100 on a test, if the maximum score on the tests is also 100, what score does the student need to maintain at least an average of 78?

Answers

(71+x)/2=78
71+x=156
x=85

Th student needs to score a min of 85

If f(x)=2x-4, find f(q+1)
please show your work!

Answers

[tex]f(q+1)=2(q+1)-4=2q+2-4=2q-2[/tex]

If the function f(x) = 2x-4, the function f(q + 1) = 2q - 2

What is a function?

A function is a mathematical equation that shows the relationship between two variables.

Since if f(x)=2x-4, to find f(q+1), we proceed as follows.

Since we have the function  f(x) = 2x - 4, and we want to find f(q + 1). To find the function f(q + 1), we substitute x = q + 1 into the equation. so, we have that

f(x) = 2x - 4

When x = q + 1, we have that

f(x) = 2x - 4

f(q + 1) = 2(q + 1) - 4

Expanding the brackets, we have that

f(q + 1) = 2q + 2 - 4

= 2q - 2

So, f(q + 1) = 2q - 2

Learn more about function here:

https://brainly.com/question/29631554

#SPJ3

The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 2 units, the value of k is ________. Numerical Answers Expected!

Answers

Answer: The value of k is 2.


Step-by-step explanation:

Given : The graph of [tex]f(x)=(0.5)x[/tex] is replaced by the graph of [tex]g(x)=0.5)x-k.[/tex]

If g(x) is obtained by shifting f(x) down by 2 units, then [tex]g(x)=(0.5)-2[/tex]

[since f(x)shifted down down by 2 , so only the value of dependent variable effect]

When we compare both functions of g(x), we found that k=2.

Hence, the value of k is 2.

The value of [tex]k[/tex] is 2.

The following information should be considered:

when [tex]g(x)[/tex] is obtained by shifting f(x) fall by 2 units so [tex]g(x) = (0.5) - 2.[/tex]Since [tex]f(x)[/tex] shifted down by 2 so there is the effect on the dependent variable. Now at the time of comparing both functions of g(x) the k should be 2.

Learn more: brainly.com/question/17429689

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