A furniture manufacturer makes two types of furniture: chairs and sofas. The production of the sofas and chairs requires three operations: carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The prfit per chair is $90 and the profit per sofa is $75. The manufacturer wants to know how many chairs and how many sofas should be produced each day to maximize the profit.
Formulate a linear programming (LP)problem you would use to find a solution.
Answer:
Chair x₁ = 10
Sofa x₂ = 18
z(max) = 2250 $
Step-by-step explanation:
Information:
Operation-Profit Carpentry Finishing Upholstery Profit
hours hours hours $
Chair (x₁) 3 9 2 90
Sofa (x₂) 2 4 10 75
Objective Function z:
z = 90*x₁ + 75*x₂
Constrains:
1.-66 hours of carpentry available
3*x₁ + 2*x₂ ≤ 66
2.- 180 hours of finishing available
9*x₁ + 4*x₂ ≤ 180
3.- 200 hours of upholstery
2*x₁ + 10*x₂ ≤ 200
Model:
z = 90*x₁ + 75*x₂ to maximize
Subject to:
3*x₁ + 2*x₂ ≤ 66
9*x₁ + 4*x₂ ≤ 180
2*x₁ + 10*x₂ ≤ 200
x₁ >= 0 x₂ >= 0
From simplex method solver we get the answer
x₁ = 10 x₂ = 18 z = 2250
The linear programming model is:
Maximize [tex]\mathbf{Z = 90x + 75y}[/tex]Subject to [tex]\mathbf{3x + 2y \le 66}[/tex], [tex]\mathbf{9x + 4y \le 180}[/tex], [tex]\mathbf{2x + 10y \le 200}[/tex], [tex]\mathbf{x,y \ge 0}[/tex]Represent sofa with y and chairs with x.
The given parameters are:
Carpentry:
[tex]\mathbf{Chair =3\ hours}[/tex]
[tex]\mathbf{Sofa =2\ hours}[/tex]
[tex]\mathbf{Available = 66\ hours}[/tex]
So, we have:
[tex]\mathbf{3x + 2y \le 66}[/tex]
Finishing
[tex]\mathbf{Chair =9\ hours}[/tex]
[tex]\mathbf{Sofa =4\ hours}[/tex]
[tex]\mathbf{Available = 180\ hours}[/tex]
So, we have:
[tex]\mathbf{9x + 4y \le 180}[/tex]
Upholstery
[tex]\mathbf{Chair =2\ hours}[/tex]
[tex]\mathbf{Sofa =10\ hours}[/tex]
[tex]\mathbf{Available = 200\ hours}[/tex]
So, we have:
[tex]\mathbf{2x + 10y \le 200}[/tex]
The profit is given as: $90 per chair, and $75 per sofa.
So, the objective function is:
[tex]\mathbf{Z = 90x + 75y}[/tex]
Hence, the linear programming model is:
Maximize [tex]\mathbf{Z = 90x + 75y}[/tex]
Subject to
[tex]\mathbf{3x + 2y \le 66}[/tex]
[tex]\mathbf{9x + 4y \le 180}[/tex]
[tex]\mathbf{2x + 10y \le 200}[/tex]
[tex]\mathbf{x,y \ge 0}[/tex]
Read more about linear programming model at:
https://brainly.com/question/13720072
44. Skiing A skier is trying to decide whether or not to buy a
season ski pass. A daily pass costs $67. A season ski pass
costs $350. The skier would have to rent skis with either pass for $25 per day. How many days
would the skier have to go skiing in order to make the season pass less expensive than
daily passes?
Determine function of the following graph
PLZ HELP DONT get wrong have 10 min HELP
Find the slope of the line that passes through (8,8) and (3,6)
simplify to fraction, improper fraction, or integer
Answer:
5.5 7
Step-by-step explanation:
Tara's website, verdantveggies.com, specializes in the sale of rare or unusual vegetable seeds. Tara sells packets of sweet-pepper seeds for $2.85 each and packets of hot-pepper seeds for $4.29 each. She also offers a 16-packet mixed-pepper assortment combining packets of both types of seeds at $3.30 per packet. How many packets of each type of seed are in the assortment?
Answer:
Let's define the variables:
S = # of sweet pepper seeds in the mix pack.
H = # of hot pepper seeds in the mix pack.
Let's suppose that $3.30 is the mean price of the seeds in the mix pack.
Then we have two equations:
S + H = 16.
(S*$2.85 + H*$4.29)/16 = $3.30
Now let's solve this system.
The first step is isolating one variable in one of the equations, i will isolate S in the first equation.
S = 16 - H.
Now we can replace this in the second equation, and solve it for H.
( (16 - H)*$2.85 + H*$4.29)/16 = $3.30
( (16 - H)*$2.85 + H*$4.29) = $3.30*16 = $52.80
$45.60 + H*$1.44 = $52.80
H*$1.44 = $52.80 - $45.60 = $7.20
H = $7.20/$1.44 = 5
Then in the mix pack there are 5 hot-pepper seeds.
And the other 11 must be sweet-pepper seeds
Algebraic equations are equations that contain unknown variables.
The number of packets of sweet-pepper seeds is 11 and the number of packets of hot-pepper seeds is 5.
Let's represent:is
The number of packets of sweet-pepper seeds = s
The number of packets of hot-pepper seeds = h
Based on this question, our system of equations are:
$2.85 x s + $4.29 x h = $3.30(16)
2.85s + 4.29h = 52.8...........Equation 1
s + h = 16...........Equation 2
s = 16 - h
We substitute 16 - h for s in Equation 1
2.85(16 - h) + 4.29h = 52.8
45.6 -2.85h + 4.29h = 52.8
Subtract 45.6 from both sides
45.6 - 45.6 -2.85h + 4.29h = 52.8 - 45.6
1.44h = 7.2
h = 5
There are 5 hot-pepper seeds in the assortment.
Solving for the number of sweet-pepper seeds.
s = 16 - h
s = 16 - 5
s = 11
There are 11 sweet-pepper seeds in the assortment.
Therefore, the number of packets of sweet-pepper seeds is 11 and the number of packets of hot-pepper seeds is 5.
To learn more, visit the link below:
brainly.com/question/12978834
which number value is in The Ten Thousands place of 272,114
Answer:
7
Step-by-step explanation:
2 is thousands so 7 must be ten thousand
Length of the rectangle is 4 less than 3 times its width. If the perimeter of
the rectangle is 32, find its length.
Answer:
The length is four less than three times the width.
x = 5 cm.
The width of rectangle is 5 cm.
Thus the length of rectangle 3x - 4 = 3 × 5 - 4 = 15 - 4 = 11 cm
Step-by-step explanation:
HOPE IT HELPS
If (2"x3mx83x90)/(15x162X912 # 48. then (m, n) is:
N
Answer:
pet for sale
Step-by-step explanation:
soory pls mark me brainbelela
Can someone plz plzzz help me out with these problems I been stuck on them for the past hour and a half
The maximum heart rate is the highest heart rate achieved during maximal exercise. In general, you get the most benefits and reduce the risks when you exercise within your target heart rate zone. Usually this is when your exercise heart rate (pulse) is about 80 percent of your maximum heart rate. The formula M = 0.8 ( 220 − A ) M = 0.8 ( 220 - A ) , gives the recommended maximum heart rate, M M , in beats per minute, for a person who is A A years of age. Determine the age of a person whose target heart rate is 128 beats per minute. The recommended maximum heart rate is 128 beats per minute for a person who is years old.
Answer:
160 years
Step-by-step explanation:
The formula for the heart rate is given by :
M=0.8 (220−A) ...(1)
M is the maximum heart rate in beats per minute and A is the age in years
Put M = 128 beats per minute in the above formula.
128=0.8(220-A)
160=220-A
A=220-160
A = 160 years
So, the age of person is 160 years if heart rate is 128 beats per munute
Answer:
B
Step-by-step explanation:
Plz give brainliest
5/6x6/7=?? Please answer
[tex] \red { \orange {\boxed {\boxed{Answer}}}}[/tex]
[tex] = \frac{5}{6} \times \frac{6}{7} [/tex][tex] = \frac{5 \times 6}{6 \times 7} [/tex][tex] = \frac{30}{42} [/tex][tex] = \frac{30 \div 6}{42 \div 6} [/tex][tex] = \frac{5}{7} [/tex]#IfWrongPleaseReport
#StudyTogetherWithMe
#ILoveMath
Simplify the complex fraction. 8/5 divide by 6 3/4 *
Step-by-step explanation:
[tex]\frac{8}{5}[/tex]÷6[tex]\frac{3}{4}[/tex]
First, simplify the 6[tex]\frac{3}{4}[/tex] to an improper fraction, which is:
[tex]\frac{27}{4}[/tex]
Next rewrite the equation using the improper fraction:
[tex]\frac{8}{5}[/tex]÷[tex]\frac{27}{4}[/tex]
Now, in order to divide the fraction, we will need to flip the second fraction over, and then multiply the two fractions together. A great way to remember this is the phrase Copy Dot Flip - Copy the first fraction, put a dot for multiplication, and flip the second fraction.
[tex]\frac{8}{5}[/tex]·[tex]\frac{4}{27}[/tex]
Finally, multiply together and simplify/reduce if needed:
The final answer is [tex]\frac{32}{135}[/tex] and no simplification or reduction is needed
how to simplify 2a³ × a⁴
Answer:
2a⁷
Step-by-step explanation:
you have to add 3 to 4
which equation represents a line which is parallel to the line x-3y=15?
Step-by-step explanation:
Two lines that are parallel have the same slope. If we make [tex]x - 3y = 15[/tex] in to slope-intercept form it'll be like this:
[tex]x - 3y = 15 \\ -3y = 15 - x \\ y = \frac{15 - x}{-3} \\ y = \frac{1}{3}x - 5[/tex]
Now we know [tex]y = \frac{1}{3}x - 5\\[/tex] as its slope-intercept form we can see the slope is [tex]\frac{1} {3}\\[/tex].
[tex]y = \frac{1}{3}x + 4\\[/tex] has the same slope as [tex]y = \frac{1}{3}x - 5\\[/tex] so they are both parallel.
Answer:[tex]y = \frac{1}{3}x + 4\\[/tex]
Jerry received 18 for his bday if he spends 7.84 to go to a movie how much will jerry have left?
I need help with 15-19 plz
Here,
g (x) = -3x + 1
then ,
g(10) = -3 (10) + 1
= -30 +1
= - 29
Again,
g(-6) = -3 (-6) + 1
= 18 + 1
= 19
Complected *******
Thank me later.
The question I need help in is the middle one. PLEASE I NEED ANDWER ASAP!
Answer:
3.25
Step-by-step explanation:
I plugged in 5 for x and got 3.25 when I solved
Haseem was given the following enlargement.
6 cm
3 cm
5 cm
22.5 cm
Figures not drawn to scale.
What is the perimeter, in centimeters, of the enlarged triangle?
0 13.5
27
O 49.5
63
Answer: The answer is 63
Step-by-step explanation:
I’m sorry I don’t know how to explain but I got it right
Answer:
63
Step-by-step explanation:
Ronald and Tim both did there laundry today Ronald does laundry laundry every 6 days and Tim does laundry every 9 days how many days will it be until Ronald and Tim both do there laundry on the same day again
Answer: 18 brainiest plz
Step-by-step explanation:
First, it is the principle of LCM (Least Common Factor) so for 6 we go 6,12,18
Then 9,18 so 18 days
Answer:
18
Step-by-step explanation:
13) What angle will a 5 meter ladder make with the ground if it reaches 4.2
meters up the wall? Round to the nearest degree.
Answer:
57°
Step-by-step explanation:
The ladder will be the hypotenuse while the 4.2 meters will be a leg.
We want the angle between the ground & the ladder. Therefore, 4.2 is on the opposite side of the angle.
sin(theta) = opposite/hypotenuse
sin(theta) = 4.2/5
theta = arcsin(4.2/5)
theta = 57°
A sandwich and a cookie cost $5.50. The cookie costs $5 less than the sandwich. How much does the cookie cost?
Answer:
.25 cents
Step-by-step explanation:
Sandwich = x
cookie = x-5
x + (x-5) = 5.50
x + x -5 = 5.50
2x = 10.50
sandwich=$5.25
cookie = (5.25) - 5
cookie = $.25
10p+5=18p–6/2 what is the value of p?
Answer:
p = 1
Step-by-step explanation:
10p + 5 = 18p - 6/2
(given)
______________
10p + 5 = 18p - 6/2
+6/2 +6/2
(addition property of equality)
_______________________
10p + 8 = 18p
-10p -10p
(subtraction property of equality
_________________________
8 = 8p
÷8 ÷8
(division property of equality)
______________________
1 = p
(symmetric property of equality)
___
p = 1
Your cell phone plan is $40 per month plus $0.10 per minute for each minute over 300 minutes of call time. Your cell phone bill came to $110.00. How many mintes did you go over your alloted timed?
Seven hundred fifty-three thousandths as a decimal
Answer:
0.753
Step-by-step explanation:
do 753/1000 and do the long division
Graph the line y=-1/3x+3
plz i need help i promise i will mark brainliest
Answer:
Step-by-step explanation:
D
Susan was supposed to use 5/4 of a cup of butter
in her recipe, but she only used 3/4 of a cup of butter.
a. What fraction of the butter that she should
have used did Susan actually use? Make a
math drawing to help you solve this problem
and explain your solution.
b. Describe the different unit amounts that occur
in part (a). Discuss how one amount can be de-
scribed with two different fractions depending
on what the unit amount is taken to be.
Answer:
[tex]a.\ \dfrac{3}{5}[/tex]
Step-by-step explanation:
We can see the fractions [tex]\frac{5}{4}[/tex] and [tex]\frac{3}{4}[/tex] of cups.
It can be seen that denominator has 4 i.e. the fraction [tex]\frac{1}{4}[/tex].
Let us suppose, a unit is equal to [tex]\frac{1}4[/tex] of a cup.
Susan was supposed to use [tex]\frac{5}{4}[/tex] of a cup.
i.e. 5 units of butter was to be used.
But, actual recipe has only 3 units of butter.
[tex]\text{Fraction of butter used} = \dfrac{\text{Units of butter used}}{\text{Unit of butter Susan was supposed to use}}[/tex]
a. [tex]\text{Fraction of butter used} = \dfrac{3}{5}[/tex]
Alternatively, we could have directly divided the given fractions:
[tex]\dfrac{\dfrac{3}{4}}{\dfrac{5}{4}} = \dfrac{3}{5}[/tex]
The fraction of the butter that she should have used did Susan actually use is :
Fractions =5/4 and 3/4 of cups.
Denominator = 4 i.e. the fraction 1/4
Let us suppose,
A unit is equal to 1/4 of a cup.
Susan was supposed to use 5/4 of a cup.
5 units of butter was to be used.
But, actual recipe has only 3 units of butter.
Fraction of butter used=unit of butter used/unit of butter
that was supposed to
be use
=3/4/5/4
=3/5
The fraction of the butter that she should have been used is 3/5.
Find out more information about "Fractions":
https://brainly.com/question/9047718referrer=searchResults
1/5t+2- =17
1/5t
.1/5t
T=
Answer:
poop i forgot my ramen noodles are in the microwave
Step-by-step explanation:
Factorise fully
14x – 8
Answer:
2(7x-4)
Step-by-step explanation:
Answer:
2(7x-4)
Step-by-step explanation:
Factor out the gratest common divisor of the coefficients of 14x - 8
Always, Sometimes, or Never?
5x>0
Answer:
Sometimes
Step-by-step explanation: