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?
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.
Write 4 3/7 as a decimal.
Enter your answer as a decimal rounded to the nearest hundredth, like this: 4.25
The decimal form of the number 4 3/7 is, 4.43
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The number is,
⇒ 4 3/7
Now, We can change in decimal form as;
⇒ 4 3/7
⇒ 31 / 7
⇒ 4.43
Thus, We get;
⇒ 4 3/7 = 4.43
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Four more than half of a number is at least nine. What is the number ?
What is 8.478 in expanded notaion
What are the factors of 60a
Answer:
20
Step-by-step explanation:
What is the quotient of 78,600 divided by 12
what is the value of x if 46=6x-2
Multiply (x – 4)(x2 – 5x – 6).
HELPZZZZZZZZZZZ PLZZZZZZZZZZZZZZ!!!!!!!
(-2)^2-(-8)*[(-2)-(-10)]
math question down below
solve the equation 5.25x+6=74.25
a relationship is linear if it has a(n) (negative, positive, constant, or undefined) rate of change.
Answer:
first one is (constant)
second answer is (slope)
the third answer is 2
Step-by-step explanation:
What are five pairs of integers with the sum of -6?
how much chocolate with each person get if 3 people share 1/2 lb of chocolate equally
Martin earned the following scores on his last five tests. 98, 78, 84, 75, 91 What is the range of his scores?
7
20
23
84
Solve the formula for the perimeter of a rectangle with width w and length l,for the length P=2w+2l solve for l
Answer:
[tex]l=\frac{P}{2}-w[/tex]
Step-by-step explanation:
we know that
The formula for the perimeter of a rectangle is equal to
[tex]P=2(w+l)[/tex]
where
l is the length
w is the width
Solve for l
That means ----> Isolate the variable l
Divide by 2 both sides
[tex]\frac{P}{2}=\frac{2(w+l)}{2}[/tex]
Simplify right side
[tex]\frac{P}{2}=w+l[/tex]
Subtract w both sides
[tex]\frac{P}{2}-w=w+l-w[/tex]
Simplify right side
[tex]\frac{P}{2}-w=l[/tex]
Rewrite
[tex]l=\frac{P}{2}-w[/tex]
Answer:Solve P = 2l + 2w for w.
The first step is to isolate the variable term, 2w.
Step-by-step explanation:
Which statement belongs in the Perimeter section of the Venn Diagram?
A.The distance around a closed figure
B.The space or region of a closed figure
C.Base and altitude is found
D.Measured in units squared
A. The distance around a closed figure is the correct answer.
Explanation:
The definition of perimeter is : The summation of the outer sides of any closed figure. Like in a rectangle, its the sum of all the four sides. In a circle, its the measure of the outline of the circle also called the circumference.
Hence, the distance around a closed figure is called its perimeter.
One of two complementary angles is 8 degrees less than the other.
Which of the following systems of equations represents the word problem?
x + y = 90 and x - y = 8
x + y = 90 and 90 - x = 8
x + y = 90 and y = 8x
Answer: The correct option is
[tex](A)~~x+y=90,~~x-y=8.[/tex]
Step-by-step explanation: Given that one of the two complementary angles is 8 degrees less than the other.
We are to select the correct system of equations represents the given word problem.
Let x and y represents the two complementary angles where y is less than x.
Since one angle is 8 degrees less than the other and y is less than x, so we have
[tex]x-y=8.[/tex]
We know that the sum of two complementary angles is 90 degrees, so we get
[tex]x+y=90.[/tex]
Thus, the required system of equations representing the given word problem will be
[tex]x+y=90,\\\\x-y=8.[/tex]
Option (A) is CORRECT.
Indicate, in standard form, the equation or inequality that is shown by the graph. (0,4)(4,0)
Answer:
standard form y = -x + b.
Step-by-step explanation:
Given : Graph and points (0,4)(4,0).
To find : Standard form of equation .
Solution : We have given that points (0,4)(4,0).
Let [tex]x_{1}[/tex] = 0 , [tex]x_{2}[/tex] = 4
[tex]y_{1}[/tex] =4 , [tex]y_{2}[/tex] = 0.
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Plugging values
Slope = [tex]\frac{0 - 4}{4 - 0}[/tex].
Slope = -1 .
Standard form y = m x + b
y = -1 x + b.
Plug (0,4)
4 = -1 ( 0)+ b
4 = b .
Now , plugging values b= 4 , m = -1.
y = -x + b.
Therefore, standard form y = -x + b.
Please Help!! find the solution of this system of equations 2x - 2y= -38 -5x - 4y= 23
y = 72.
Solving the System of Equations
To find the solution of the system of equations given by 2x - 2y = -38 and -5x - 4y = 23, we can use the method of elimination or substitution. In the method of elimination, we can multiple the first equation by 2 to make the coefficients of y the same, which would give us 4x - 4y = -76. Then, we could add this new equation to the second given equation (-5x - 4y = 23) to eliminate the y variable:
4x - 4y = -76 (First equation multiplied by 2)
-5x - 4y = 23 (Second given equation)
Adding these equations together, we get:
-1x + 0y = -53
or simply
-x = -53, from which x = 53.
Next, we can substitute x back into either of the original equations to solve for y. For example, using 2x - 2y = -38:
2(53) - 2y = -38
106 - 2y = -38
-2y = -38 - 106
-2y = -144
y = 72
Therefore, the solution to the system of equations is x = 53 and y = 72.
K(-5,-2), M(5,4), S(-3,6), T(3,-4)
8 = x divided by 12.8
Gary mails 10 to 3 power flyers to clients in one week. How many flyers does Gary mail
Solve for x
3x + 3 − x + (−7) > 6
Consider the following set of equations:
Equation A: y = −x + 5
Equation B: y = 6x − 2
Which of the following is a step that can be used to find the solution to the set of equations?
−x = 6x + 2
−x − 2 = 6x + 5
−x + 5 = 6x – 2
−x + 5 = 5x
Answer:
C)
Step-by-step explanation:
both of the equations equal y so, the two equations equal eachother
You are making bouquets to sell. You have 60 roses, 84 daisies, and 24 lilies. Each bouquet will have the same number of each kind of flower. You want to use all of the flowers. What is the greatest number of bouquets you can make?
Answer:
you can make 12 bouquets...each containing 5 roses, 7 daisies, and 2 lilies
Step-by-step explanation:
I need help with this question
Linda made $238 for 17 hours of work.
At the same rate, how many hours would she have to work to make $168?
Tara makes the following statement: "There is a 70% chance of sunny weather tomorrow and a 60% chance I will go to the beach." What is the probability that it will be sunny tomorrow and Tara will go to the beach? 42% 22% 11% 13%
Answer:
The probability is 42%
Step-by-step explanation:
The probability that A and B, two independent events, happens is given by:
P=P(A)*P(B)
In this case, lets call A the event in which there are sunny weather tomorrow and B the event in which Tara goes to the beach. Taking into account that they are independent, that means that one event doesn't affect the other, the probability P that it will be sunny tomorrow and Tara will go to the beach is:
P=0.7*0.6=0.42
Multiplying P by 100, we get:
P=42%
So, the probability that it will be sunny tomorrow and Tara will go to the beach is 42%