Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary style cabinets sell for $90 and farmhouse style cabinets sell for $85. Each cabinet produced must go through carpentry, painting, and fiishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet.
Hours per process
Style Carpentry Painting Finishing
Contemporary 2.0 1.5 1.3
Farmhouse 2.5 1.0 1.2
Carpentry costs $15 per hour, painting costs $12 per hour, and fiishing costs $18 per hour, and the weekly number of hours available in the processes is 3000 in carpentry, 1500 in painting, and 1500 in fiishing. Brooklyn also has a contract that requires the company to supply one of its customers with 500 contemporary cabinets and 650 farmhouse style cabinets each week.
Let
x = the number of contemporary style cabinets produced each week
y = the number of farmhouse style cabinets produced each week
Develop the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit.
The objective function is maximize
Show the mathematical expression for each of the constraints on the three processes.
Hours available in carpentry: x1 + y1 ≤
Hours available in painting: x2 + y2 ≤
Hours available in fiishing: x3 + y3 ≤
Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements.
x ≥
y ≥
Answer:
See Step by step explanation
Step-by-step explanation:
Objective Function: z
x = number of contemporary style
y = number of farmhouse style
Costs
Carpentry costs:
15*2*x + 15*2,5*y = 30*x + 37,5*y
Painting costs
12*1,5*x + 12*1*y = 18*x + 12*y
Finishing costs
18*1,3*x + 18*1,2*y = 23,4*x + 21,6*y
Total costs:
30*x + 37,5*y + 18*x + 12*y + 23,4*x + 21,6*y
71,4*x + 71,1*y
z = 90*x + 85*y - ( 71,4*x + 71,1*y ) to maximize
z = 18,6*x + 13,9*y to maximize
Subject to:
First constraint:
Hours available in carpentry 3000
2*x + 2,5*y ≤ 3000
Second constraint
Hours available in painting 1500
1,5*x + 1*y ≤ 1500
Third constraint
Hours available in finishing 1500
1,3*x + 1,2*y ≤ 1500
Fourth constraint
Minimum quantity of contemporary style 500
x ≥ 500
Fifth constraint
Minimum quantity of farmhouse style 650
y ≥ 650
General constraints:
x ≥ 0 y ≥ 0 x , y integers
Model:
z = 90*x + 85*y - ( 71,4*x + 71,1*y ) to maximize
Subject to:
2*x + 2,5*y ≤ 3000
1,5*x + 1*y ≤ 1500
1,3*x + 1,2*y ≤ 1500
x ≥ 500
y ≥ 650
x ≥ 0 y ≥ 0 x , y integers
The mathematical expression for each of the constraints on the three processes.
Model z = 90*x + 85*y - ( 71,4*x + 71,1*y )
Subject to
2*x + 2,5*y ≤ 3000
1,5*x + 1*y ≤ 1500
1,3*x + 1,2*y ≤ 1500
x ≥ 500
y ≥ 650
x ≥ 0 y ≥ 0 x , y integers.
We, wants to maximize the total weekly profit.
What is the meaning of constraints?a constraint is a condition of an optimization problem that the solution must satisfy.
Objective function: z
x = number of contemporary style
y = number of farmhouse style
We have to find the cost
The carpentry costs is,
15*2*x + 15*2,5*y = 30*x + 37,5*y
The painting costs is
12*1,5*x + 12*1*y = 18*x + 12*y
The finishing costs is
18*1,3*x + 18*1,2*y = 23,4*x + 21,6*y
Therefore the total costs is,
30*x + 37,5*y + 18*x + 12*y + 23,4*x + 21,6*y
71,4*x + 71,1*y
z = 90*x + 85*y - ( 71,4*x + 71,1*y ) to maximize
z = 18,6*x + 13,9*y to maximize
Subject to the constraint;
The first constraint is,
The hours available in carpentry 3000
2*x + 2,5*y ≤ 3000
The second constraint is,
Hours available in painting 1500 so,
1,5*x + 1*y ≤ 1500
The third constraint is,
Hours available in finishing 1500 so,
1,3*x + 1,2*y ≤ 1500
Fourth constraint is,
The minimum quantity of contemporary style 500 so,
x ≥ 500
The fifth constraint is
The minimum quantity of farmhouse style 650 so,
y ≥ 650
The general constraints are,
x ≥ 0 y ≥ 0 x , y integers,
Therefore the Model z = 90*x + 85*y - ( 71,4*x + 71,1*y ) to maximize,
Subject to
2*x + 2,5*y ≤ 3000
1,5*x + 1*y ≤ 1500
1,3*x + 1,2*y ≤ 1500
x ≥ 500
y ≥ 650
x ≥ 0 y ≥ 0 x , y integers,
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https://brainly.com/question/6073946
ON wednesday Eddy goes to a velodrome to train. He cycles the first lap of the track in 25 seconds. Each lap Eddy cycles takes him 1.6 seconds longer thatn the previous lap.
Required:
a. Find the time in seconds, Eddy takes to cycle his tenth lap 2
b. Eddy cycles his last lap in 55.4 seconds. Find how many laps he has cycled on wednesday.
c. Find the total time in minutes, cycled by Eddy on Sunday.
Answer:
Step-by-step explanation:
The data of timing for each lap will form a arthmetic progression ( AP ) with first term as 25 s and common difference of 1.6 s .
a )
first term a = 25
common difference d = 1.6 .
10 th term of the series can be given by following formula
a₁₀ = 25 + ( 10-1 ) x 1.6
= 25 + 1.6 x 9
= 39.4 s
b )
Let n th be the last lap
a(n) = a + ( n-1 ) x d
55.4 = 25 + ( n- 1 ) x 1.6
n - 1 = 19
n = 20 .
c )
sum of all the term of AP
=( first term + last term ) x no of term / 2
= (25 + 55.4 ) x 20 / 2
= 804 s .
= 804 / 60 min
= 13.4 min .
Name the integers and the rational numbers in the given set. {-2,5, √6, 2/3,π Select the correct choice below and fill in any answer boxes within your choices. whts the answer ?
How do you find area of a trapezoid I will mark brainliest for the most explained and simple answer!!!!
Answer:
A = ((a+b)/2)h
Step-by-step explanation:
a and b are base (the top and bottom)
h is height
Light travels about 180,000,000 km in 10 minutes how far does it travel in one second?
Answer:
I think it is 300000 per second so what i did is converted the 10 minutes to seconds which is 600 and then divided 180,000,000 which gave me 300000 if you wanna see if it correct then just multiply 300000 by 600
NEED HELP THANKS IN ADVANCE.
Answer:
b
Step-by-step explanation:
Answer:
3x^5 - 5x^3+2x^2-10x +4 = 4x^4 + 6x^3-11can be solved by using this system of equations.
Two pizzas and four sandwhiches cost $62. Four pizzas and ten sandwiches cost $140. how much does each pizza and sandwhich cost?
Answer:
Pizzas are $15
Sandwiches are $8
Step-by-step explanation:
Write a system of equations
Pizza = x
Sandwiches = y
2x + 4y = 62
4x + 10y = 140
Isolate a variable in one of the equations
2x = 62 - 4y
x = 31 - 2y
Plug isolated x value into other equation
4(31-2y) +10y = 140
124 - 8y + 10y = 140
Simplify
2y = 16
y = 8
Plug y value into equation to solve for x
2x + 4(8) = 62
2x + 32 = 62
2x = 30
x = 15
An experiment started with 100 bacteria. they double in number every hour. find the number of bacteria after 6 hours.
I need some help with this
How do u solve this plzzzz helppp
It’s called multi step equations
Answer:
x=6
Step-by-step explanation:
7x-9=3x+15
4x-9=15
4x=24
x=6
Answer:
x=6
Step-by-step explanation:
7−9=3+15
7−9+9=3+15+9
7−3=3+24−3
4=24
x=6
HELP ME PLEASEEEWWWW
Answer:
ahhhhhh
Step-by-step explanation:
Answer:
i think its the second one sorry if im wrong
Step-by-step explanation:
anyone please this answer fast for grade6
Answer:
1 round = 220 meter wire
2 rounds = 440 meter wire
3 rounds = 660 meter wire
Step-by-step explanation:
Given that:
Perimeter of squared garden = 220m
As the perimeter is given, the length of the wire would be calculated with it.
The length of wire to fence with 1 round = 220 * 1 = 220m
The length of wire to fence with 2 rounds = 220 * 2 = 440m
The length of wire to fence with 3 rounds = 220 * 3 = 660m
Hence,
1 round = 220 meter wire
2 rounds = 440 meter wire
3 rounds = 660 meter wire
What is the product?
4927 x 7
Answer:
34489
Step-by-step explanation:
HELP ASAP. WILL GIVE BRAINLIEST
Answer:
15 x p = 300 OR 15p = 300
Step-by-step explanation:
Find the general solution of
dy/dx + 2y =6
Answer:
ye^(2x) - 3e^(2x) = C or (y - 3)e^(2x) = C
Step-by-step explanation:
dy/dx + 2y = 6
This is a first order linear ODE.
p(x) = 2
Integrating factor: I(x) = e^(∫ 2 dx) = e^(2x)
e^(2x)(dy/dx + 2y) = 6e^(2x)
e^(2x) dy + 2ye^(2x) dx = 6e^(2x) dx
Integrate both sides of the equation.
ye^(2x) = 3e^(2x) + C
Thus, the general solution is ye^(2x) - 3e^(2x) = C or (y - 3)e^(2x) = C.
Is 0.456 greater than or less than 0.5
Answer:
0.456 is less than 0.5
Step-by-step explanation:
Does anyone know the answer to this question??
help me with this question, thanks!!!
Answer:
Gavin is incorrect,
divide 4
multiply 1/4
each get 1/12
Step-by-step explanation:
AC = 3x + 6 and CD = 2x + 14. Find x
Answer:
x= 8
Step-by-step explanation:
3x+6=2x+14
=8
put the equations together like previously shown. and combine like terms to solve for x
Simplify
(4x+2)+(x-1)=
Answer:
5x+1
Step-by-step explanation:
(4x+2)+(x-1)=
Combine like terms
4x+x +2 -1
5x+1
The quotient of 56 and n is multiplied by 3.
Create an equivalent expression using n to represent the unknown number.
Answer:
Equivalent expression using n to represent the unknown number is: [tex]\mathbf{(\frac{56}{n})\times 3\\}[/tex]
Step-by-step explanation:
The quotient of 56 and n is multiplied by 3.
Create an equivalent expression using n to represent the unknown number.
We need to write equivalent expression of The quotient of 56 and n is multiplied by 3.
We will do this step by step
First we will find:
The quotient of 56 and n
It can be written in mathematical form is: [tex]\frac{56}{n}\\[/tex]
Now, we will find
The quotient of 56 and n is multiplied by 3.
It can be written in mathematical form as: [tex](\frac{56}{n})\times 3\\[/tex]
So, equivalent expression using n to represent the unknown number is: [tex]\mathbf{(\frac{56}{n})\times 3\\}[/tex]
If you are able to save, $150 dollars per month-how many months will it take you to
save $2,500 dollars.
HELP ME
Answer:
16.66months
Step-by-step explanation:
2500/150
Ahmed wrote two numbers. The first number has a 7 in its tenth place. The second number has a 7 with a value that’s is 1,000 times greater than the value of the 7 in the first number. In which place is the 7 in the second number?
Answer:
in the thousands place
Step-by-step explanation:
Answer:
Hundreds
Step-by-step explanation:
Ahmed wrote two numbers.The first number has 7 in it's tenth place.The second number has a 7 with a value that's 1,000 times greater than the value of the 7 in the first number.This is how we can represent it:
*The symbol 'x' represents the numbers that we don't know.
7xx.7
The first 'x' has a place value of ones.
The second 'x' has a place value of tens.
And the second number (7) has a place value of hundreds.
(5,3) reflected across the x axis and then across the y axis
Answer: (-5,-3)
Step-by-step explanation:
Answer:
X-axis: (5, -3)
Y-axis: (-5, 3)
Step-by-step explanation:
Find the slope of the line that contains the points (1, 6) and (10, -9)
Answer:
-15/9
Step-by-step explanation:
The slope is the steepness of the line. To find it, you divide how far up it goes by how far across it goes. This equals the diagonal incline. To find it with points, you find the difference between the y values and divide that by the difference in the x values!
-9-6=-15
10-1=9
-15/9=-15/9
This slope means that for every nine units the line goes across, it goes down 15 units!
Have a wonderful day :D
Mr Binnix wife is older than her sister by 2 years if their ages add up to 52 how old is each sister? Let c represent Leigh Ann’s age and let y represent Larisa s age
Answer:
the older sister is 27 and the younger is 25.
Step-by-step explanation:
C+2=Y
C+Y=52
2C+2=52
2C=50
C=25
25+2=Y
Y=27
what is the slope intercept form of the equation of the line?
Answer:
The slope-intercept form of the equation of the line is:
y = 2/3x + 2
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
m is the slopeb is the y-interceptGiven the points
(0, 2)(3, 4)(x₁, y₁) = (0, 2)
(x₂, y₂) = (3, 4)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [4 - 2] / [3 - 0]
= 2 / 3
Thus, the slope of the line = m = 2/3
We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
From the graph, it is clear
at x = 0, y = 2
Thus, the y-intercept b = 2
now substituting m = 2/3 and b = 2 in the slope-intercept form
y = mx+b
y = 2/3x + 2
Therefore, the slope-intercept form of the equation of the line is:
y = 2/3x + 2
Tina collects stuffed animals. She has 8 teddy bears, 9 dogs, 10 frogs, and 6 monkeys. What is the ratio of monkeys to teddy
bears?
A. 3:7
B. 3:4
O C. 8:6
O D. 7:4
Plssss help ASAP giving away lost of branlist
Answer:
it's c
Step-by-step explanation:
there are 8 bears and 6 monkeys!
hope this helps:)
What is 1/5 expressed as a percent?
Find the radius of a circle with a circumference of 68.2
(pi = 3.1 NOT 3.14)
Answer:
646.4
Step-by-step explanation:
Answer:
d= 22
Step-by-step explanation:
C=πd
68.2= 3.1*d
68.2 / 3.1 =22
d=22