The optimal point in order to get the maximum profit is 1550.
Given constraints are:
x + 2y ≤ 40 ........(1)
4x + 3y ≤ 120 .........(2)
x≥ 10, y ≥ 10
Now, we need to find the optimal point in order to get the maximum profit.
Maximize Z=50x + 60y
Let's put the value of y = 10 in the given equation
Maximize Z=50x + 60(10)
Z = 50x + 600 ........(3)
Now, we will convert equations (1) and (2) in terms of x only as follows:
x ≤ 40 - 2y
x ≤ 30 - 3/4y
Substituting x = 10, we get:
y ≤ 15
x = 10,
y = 15 satisfies all the constraints.
Now, substituting these values in equation (3), we get:
Z = 50(10) + 60(15)
Z = 1550
Therefore, the maximum profit is 1550.
To know more about profit,
https://brainly.com/question/26483369
#SPJ11
What is the result of subtracting the second equation from the first?
-4x-2y=-2
x-2y=9
Answer:
x=2.2
y=-3.4
Step-by-step explanation:
subtract the second from the first
-5x=-11
x=2=2
substituting by x in the first equation
so y=-3.4
Use the CVP Formulas to solve the following. JBL Speakers has annual fixed costs of $2,450,000, and variable costs of $25 per unit. The selling price per unit is $90. A) What annual revenue is required to break even? BER B) What annual unit sales are required to make a $1,000,000 profit?
Using the CVP Formulas to solve the following. JBL Speakers has annual fixed costs of $2,450,000, and variable costs of $25 per unit. The selling price per unit is $90.
A) 37,692 units
B) 53,077 units
A) To calculate the annual revenue required to break even, we need to find the point where total revenue equals total costs.
Total cost (TC) = Fixed costs (FC) + Variable costs per unit (VC) * Quantity (Q)
Total revenue (TR) = Selling price per unit (SP) * Quantity (Q)
At the break-even point, total revenue equals total cost:
TR = TC
SP * Q = FC + VC * Q
Substituting the given values:
$90 * Q = $2,450,000 + $25 * Q
$90Q - $25Q = $2,450,000
$65Q = $2,450,000
Q = $2,450,000 / $65
Q ≈ 37,692.31
Therefore, approximately 37,692 units need to be sold to break even.
B) To calculate the annual unit sales required to make a $1,000,000 profit, we can use the following formula:
Profit (P) = (SP * Q) - (FC + VC * Q)
Substituting the given values and the desired profit:
$1,000,000 = ($90 * Q) - ($2,450,000 + $25 * Q)
$90Q - $25Q = $1,000,000 + $2,450,000
$65Q = $3,450,000
Q = $3,450,000 / $65
Q ≈ 53,076.92
Therefore, approximately 53,077 units need to be sold to make a $1,000,000 profit.
In conclusion, to break even, JBL Speakers needs to generate an annual revenue of approximately $2,450,000, and to make a $1,000,000 profit, they need to sell approximately 53,077 units annually.
To know more about variable , visit :
https://brainly.com/question/29192928
#SPJ11
A rectangle has a perimeter of 150 cm. The length is 3 cm more than twice the width. Find the length and width of the rectangle.
Answer:
Length of rectangle = 51 cm
Width of rectangle = 24 cm
Step-by-step explanation:
Given:
Perimeter of rectangle = 150 cm
Find:
Length and width of the rectangle
Computation:
Assume;
Width of rectangle = a cm
Length of rectangle = 2a + 3 cm
Perimeter of rectangle = 2[l + b]
150 = 2[(2a + 3) + a]
2[3a + 3] = 150
6a + 6 = 150
6a = 144
a = 24
Width of rectangle = 24 cm
Length of rectangle = 2a + 3 cm
Length of rectangle = 2(24) + 3 cm
Length of rectangle = 51 cm
Solve the inequality for d
df+9h>2
Answer:
d=2_f - 9h_f
Step-by-step explanation:
es la segunda opción
Can I get help with number 20
Answer:
-5/4
Step-by-step explanation:
GIVING BRAINLIEST!!!!!!
Answer:
y+x = -4
Step-by-step explanation:
-4 indicates where the line intercept the y axis
if we put y=0 we can find where line intercepts the x axis.
it results x = -4
the two values are negative
Find the volume of each figure. Round the answer
5 min
4 mm
18 nm
8 mm
Your friend Sam wants to paint her room. She wants to paint the ceiling
white and the four walls purple.
You are helping Sam determine the cost and the amount of time needed to
paint her room.
The room is shaped like a rectangular prism with a height of 8 feet, length of
12 feet, and width of 10 feet as shown.
one hundred and twenty approximately
An object completes one round of circle of radius 7m in 20 sec. find the distance travelled after 10sec.
Answer: 7pi
Step-by-step explanation: If it completes the circumference distance (14pi) of the circle in 20 seconds, in 10 seconds it will complete half of that. or 7pi. Hope this helped!
:.the distance travelled after 10sec. =7πm
Answer:
in 20 sec distance travelled =2πr=2π×7=14πm
in 10 sec distance travelled=14πm×10/20=7πm
What is the greatest common factor of the numbers
15,30 , and 75 ?
Answer:
15
Step-by-step explanation:
Prime Numbers Check
15: 5 * 3
30: 2 * 3 * 5
75: 3 * 5 * 5
Both 3 and 5 are prime numbers present in all 3 greater numbers, then you multiply them
3*5 = 15
GCF is 15
How does the graph of the
function g(x) = 2* + 6 differ from
the graph of f(x) = 2*?
Answer:
YUH
Step-by-step explanation:
Answer:
you'll see...
Step-by-step explanation:
Given that the transformed graph is of function f(x) = (x + 2)^4 + 6 and the parent function g(x) = x^4
The transformed graph function g(x) was shifted two (2) units to the left and was translated six (6) units upward.
When the function is shifted to the right, the factor of x will be negative and when it's shifted to the left, the factor of x will be positive.
Therefore, function g(x) = x^4 is shifted 2 units to the left and translated 6 units upward to form f(x) = ( x + 2 )^4 + 6.
Which of the following points lies on the line 2x+3y=5?
Give an example to show that when two prime numbers are added, the result
may be an odd number.
Answer:
2+3=5
Step-by-step explanation:
prime numbers =2 and 3
sum =5 which is odd
In the expression 8k + 5. which best describes what 8 represents?
Answer:
it represents a variable
Step-by-step explanation:
The number 8 is the coefficient of the variable k.
What is a coefficient?A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.
Given that the expression is 8k + 5. In the given expression the number 8 is the coefficient of the given expression.
To know more about coefficient follow
https://brainly.com/question/17469127
#SPJ6
The first term in an arithmetic sequence is 5. The fourth term in the sequence is −4. The tenth term
is −22.
Which function can be used to find the nth term of the arithmetic sequence?
Answer:
aₙ = -3n + 8Step-by-step explanation:
The nth term of an arithmetic sequence: aₙ = a₁ + d(n - 1)
{d = common difference}
a₁ = 5
a₄ = 5 + d(4 - 1)
-4 = 5 + 3d
-4 - 5 = 3d
3d = -9
d = -3
Therefore;
aₙ = 5 + (-3)(n - 1)
aₙ = -3n + 8
Check: a₁₀ = 5 + (-3)(10 - 1) = 5 - 27 = - 22
The nth term of the sequence is Tn = 8 - 3n
How to determine the function of the nth term?The given parameters are:
a = 5, first term
T4 = -4 --- the 4th term
T10 = -22 --- the 10th term
The nth term of an arithmetic sequence is:
Tn = a + (n - 1) * d
So, we have:
T4 = a + (4 - 1) * d
Substitute known values
-4 = 5 +(4 -1) * d
This gives
-4 = 5 + 3d
Subtract 5 from both sides
3d = -9
Divide by 3
d = -3
Recall that:
Tn = a + (n - 1) * d
So, we have:
Tn = 5 + (n - 1) * -3
Expand
Tn = 5 + 3 - 3n
Solve
Tn = 8 - 3n
Hence, the nth term of the sequence is Tn = 8 - 3n
Read more about arithmetic sequence at:
https://brainly.com/question/6561461
Express the function G in the form f o g. (There is more than one correct answer. The function is of the form y = f(g(x)). Use non-identity functions for f(x) and g(x).)
G(x) = 1/x+8
(f(x), g(x) = ([_________])
To express the function [tex]\(G\)[/tex] in the form [tex]\(f \circ g\)[/tex] , where [tex]\(y = f(g(x))\)[/tex] , we need to find suitable non-identity functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x)\)[/tex].
Let's choose [tex]\(g(x) = \frac{1}{x}\)[/tex] and [tex]\(f(x) = x + 8\)[/tex].
Now, we can express [tex]\(G\)[/tex] as [tex]\(G(x) = f(g(x))\)[/tex] , which becomes:
[tex]\[G(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \frac{1}{x} + 8\][/tex]
Therefore, the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x) = \frac{1}{x} + 8\) are \(f(x) = x + 8\)[/tex] and [tex]\(g(x) = \frac{1}{x}\)[/tex].
To know more about probabilities visit-
brainly.com/question/32512587
#SPJ11
139°
(17x + 3)
answer
Answer:
x= 8
Step-by-step explanation:
17x + 3 = 139
17x = 136
x = 8
The count of bacteria in a certain experiment was increasing at a rate of 2.5% per hour. if the experiment started with 1600. find the count of the bacteria at the end of 22 hours.
DONT ADD ANY LINK PLEASE I WILL REPORT AND PLEASE ANSWER CORRECTLY AND FAST I WILL MARK BRAINLIEST
a strain of peas has 3 green and one yellow for every four peas. if 12 peas are rendomly selected, what is the probability that exactly 8 peas are green? provide your answer to three decimal places
The probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.
We can use the binomial probability formula to solve this problem.
The formula is given as; $$P(X=k)={n\choose k}p^k(1-p)^{n-k}$$
Where;
n= sample size=12
k= number of green peas=8
p= probability of getting a green pea=3/4
q= probability of getting a yellow pea=1/4
Since we want the probability of exactly 8 green peas out of 12 peas,
we will plug in the values in the formula to get;
$$P(X=8)={12\choose 8}(\frac{3}{4})^8 (1-\frac{3}{4})^{12-8}$$$$
P(X=8)={12\choose 8}(\frac{3}{4})^8(\frac{1}{4})^{4}$$$$P(X=8)=495
(0.3164)(0.0039)$$$$P(X=8)=0.4749$$
Therefore, the probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.
know more about binomial probability
https://brainly.com/question/12474772
#SPJ11
Dean wants to buy a scooter. He has a coupon for 20% off his purchase, and has already saved $50. If the scooter is $79, how much more money does Dean need to be able to purchase it?
4) A spinner has 8 congruent sections as shown in the diagram. If the
spinner is spun twice, what is the probability that the first spin will land on
a whistle and the second spin will land on a yo-yo?"
a. 1/2
b. 1/8
c. 2/8
d. 1/32
HELP ME PLS
how do you graph a function??????
Answer:
It depends on the type of function, but essentially the process is the same
Step-by-step explanation:
You gather up all of the y values and x values and plot them onto a coordinate grid. If you are using a calculator, go to the "y=" button and input the function and then hit "graph"
Este año en la escuela de inglés, el numero de usuarios de intagram ha alcanzado la cifra de 2604 alumnos, lo que supone un aumento del 24% respecto del año pasado. ¿ cuantos usuarios habia el año pasado?
Answer:
the number of users in the last year is 2,100
Step-by-step explanation:
The computation of the number of users in the last year is shown below:
Given that
The users are 2604 that are increased to 24% as compared with the last year
So, the users in the last year is
= 2604 ×100 ÷ 124
= 2,100
Hence, the number of users in the last year is 2,100
Answer:
688
Step-by-step explanation:
ithink
at time t = 0 the capacitor in the circuit below is fully charged with qmax, and the current through the circuit is 0.
At time t = 0, the capacitor in the circuit is charged to its maximum charge, qmax, and the circuit has zero current.
At t = 0, the capacitor in the circuit is fully charged, which means it has accumulated its maximum charge, qmax. The capacitor acts as a temporary energy storage device in the circuit. When the capacitor is fully charged, it contains potential energy. The charge on the capacitor creates an electric field, which opposes the flow of current through the circuit.
Since the capacitor is fully charged at t = 0, it resists any change in the current. Therefore, the circuit has zero current flowing through it. As time progresses, the capacitor will start to discharge, releasing the stored energy and allowing the current to flow. The discharge process is governed by the relationship between the voltage across the capacitor, the capacitance of the capacitor, and the resistance in the circuit.
Finally, at t = 0, the capacitor in the circuit is charged to its maximum capacity, qmax, and the circuit has zero current flowing through it.
Learn more about time here:
https://brainly.com/question/1649360
#SPJ11
The hair color of the players on a tennis team would be considered: a. Ratio data b. Ordinal data c. Nominal data d. Interval data
The hair color of the players on a tennis team would be considered nominal data. Therefore, the most appropriate answer is option (c): Nominal data.
In data classification, there are four main levels of measurement: nominal, ordinal, interval, and ratio. Nominal data is the lowest level of measurement and represents categories or labels that cannot be ranked or ordered. Hair color falls into this category as it represents different categories or labels such as blonde, brunette, red, etc. Nominal data does not have any inherent numerical value or order.
On the other hand, ordinal data represents categories that can be ordered or ranked but do not have a consistent interval between them. Interval and ratio data involve numerical values with a consistent interval and a true zero point, with ratio data having a meaningful zero point.
To know more about ratio click here: brainly.com/question/13419413 #SPJ11
I need help plzzz
-6p + 19 > 7
Answer:
p < 2
Step-by-step explanation:
hope this is right and have a good day
Factor this expression completely and then placed the factors in the proper location on the grid. Note: please factors alphabetically in the grid!
ab + 4 + a + 4b
PLEASE ANSWER, WILL MARK BRAINLYEST!
Answer:
(a + 4)(b + 1)
Step-by-step explanation:
ab + 4 + a + 4b
Rearrange the expression to find the GCF.
ab + a + 4b + 4
Now find the GCF.
a (b + 1) + 4 (b + 1)
Divide the whole thing by b+1
(a + 4)(b + 1)
guys can you help me answer this?
6. The table shows the number of manatee deaths caused by watercraft in Florida each year
beginning in 1980. The years are coded that 1980 is 1, 1981 is 2, and so on. Use the table to
find the best model and the R2 value.
Year
1
2
3
4
5
6
7
8
9
10
Deaths
16
24
20
15
34
33
33
39
43
50
(1 point)
linear model, 0.845
exponential model, 0.779
power model, 0.682
quadratic model, 0.866
Answer: quadratic model, 0.866
Step-by-step explanation:
HELP MATH ASAP! I GIVE BRAINLIEST