The following table pertains to Pieway, an economy in which the typical consumer's basket consists of 10 bushels of apples and 6 bushels of almond .
Answers
Pieway is an economy in disequilibrium. The prices of apples and almonds are below the equilibrium prices, resulting in an excess demand for both goods. If producers increase their prices, then the consumer's expenditure will also increase.
What is price?Price is the amount of money that a person needs to pay in order to purchase a product or service. It is the amount of money that a consumer is willing to pay for a good or service. Price is determined by the seller, or by the market forces of supply and demand. The price of a product or service can be influenced by factors such as competition, availability, quality, and demand.
Price of Apples (per bushel) Price of Almond (per bushel) Consumer's Expenditure
$2 $4 $48
Pieway is a small economy with a small population and limited resources. The prices of apples and almonds are determined by the demand and supply in the market. In this economy, the prices of apples and almonds are fixed, and the consumer's expenditure is fixed at $48. The prices of apples and almonds are below the equilibrium prices, so there is an excess demand for both apples and almonds in the market.
The market is in disequilibrium and the quantity demanded of apples and almonds is greater than the quantity supplied. Consumers will be willing to pay more for apples and almonds than their current prices. As a result, producers are likely to increase the prices of apples and almonds in the market. Consequently, the consumer's expenditure will increase to higher than the current level of $48.
In conclusion, Pieway is an economy in disequilibrium. The prices of apples and almonds are below the equilibrium prices, resulting in an excess demand for both goods. If producers increase their prices, then the consumer's expenditure will also increase.
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Related Questions
Wellington has $21 to ride bumper cars and play games at the count fair. Suppose the bumper cars cost $3.50. Write and solve an inequality to find the most he can spend on games.
Answers
Answer: 17.50
Step-by-step explanation:
-4/7x -8/21x + 1/3x =-65
Answers
Answer:
x=105
Step-by-step explanation:
Given the speeds of each runner below, determine who runs the fastest.
\text{Jessica runs 10 feet per second.}
Jessica runs 10 feet per second.
\text{Jake runs 507 feet in 39 seconds.}
Jake runs 507 feet in 39 seconds.
\text{Tony runs 1 mile in 541 seconds.}
Tony runs 1 mile in 541 seconds.
\text{Stephanie runs 703 feet in 1 minute.}
Stephanie runs 703 feet in 1 minute.
Answers
Answer:
Step-by-step explanation:
jake runs the fastest
Jake is the fastest runner among Jessica, Jake, Tony, and Stephanie.
Here, we have,
To determine who runs the fastest, we need to compare the speeds of Jessica, Jake, Tony, and Stephanie.
First, let's convert all the given distances to feet per second, which will allow us to directly compare their speeds.
1 mile is equal to 5280 feet.
Now, let's calculate the speeds for each runner:
Jessica: 10 feet per second (already given)
Jake: Jake runs 507 feet in 39 seconds, so his speed is 507 feet / 39 seconds ≈ 13 feet per second.
Tony: Tony runs 1 mile (5280 feet) in 541 seconds, so his speed is 5280 feet / 541 seconds ≈ 9.76 feet per second.
Stephanie: Stephanie runs 703 feet in 1 minute (60 seconds), so her speed is 703 feet / 60 seconds ≈ 11.72 feet per second.
Comparing the speeds, we can see that Jake runs the fastest with a speed of approximately 13 feet per second.
Therefore, Jake is the fastest runner among Jessica, Jake, Tony, and Stephanie.
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Derwin purchased a computer for $598.95, software for $128.88, and a wireless mouse for $14.95. Derwin will make equal payments for 6 months. Approximately how much will he pay each month?
Answers
Answer:
its 121.31
Step-by-step explanation:
we wish to construct a rectangular auditorium with a stage shaped as a semicircle of radius $r$, as shown in the diagram below (white is the stage and green is the seating area). for safety reasons, light strips must be placed on the perimeter of the seating area. if we have $45\pi 60$ meters of light strips, what should $r$ be so that the seating area is maximized?
Answers
To maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.
To maximize the seating area, we need to determine the dimensions of the rectangular auditorium that will give us the largest possible area while using the given length of light strips.
Let the length of the rectangular auditorium be L, and its width be W.
The seating area consists of the rectangular portion minus the semicircular stage. So, the seating area's length is L - 2r (subtracting the semicircle's diameter) and the seating area's width is W - 2r.
The perimeter of the seating area is the sum of the lengths of its four sides, excluding the semicircular stage. The perimeter is given as 45π + 60 meters.
Perimeter = 2(L - 2r) + 2(W - 2r) + πr = 45π + 60
Simplifying: 2L + 2W - 8r + πr = 45π + 60
Rearranging: 2L + 2W = 8r + 44π + 60
The area of the seating area is given by A = (L - 2r)(W - 2r).
We want to maximize A, so we need to express it in terms of a single variable. Since we have an equation with two variables (L and W), we can rewrite one of the variables in terms of the other.
Rearranging the perimeter equation: 2L + 2W = 8r + 44π + 60
Solving for L: L = (8r + 44π + 60 - 2W) / 2
Substituting L in terms of W into the area equation: A = [(8r + 44π + 60 - 2W) / 2 - 2r] (W - 2r)
Simplifying: A = (4r + 22π + 30 - W) (W - 2r)
Now we have the area equation in terms of a single variable, W. To maximize A, we can take the derivative of A with respect to W, set it equal to zero, and solve for W.
dA/dW = 2(4r + 22π + 30 - W) - (W - 2r) = 0
Solving for W: 8r + 44π + 60 - W = W - 2r
Simplifying: 10r + 44π + 60 = 2W
W = 5r + 22π + 30
Now that we have W in terms of r, we can substitute this expression back into the area equation to get the area in terms of r only.
A = (4r + 22π + 30 - (5r + 22π + 30)) ((5r + 22π + 30) - 2r)
Simplifying: A = (r - 22π) (3r + 22π + 30)
Expanding: A = 3r² + 8rπ + 30r - 66πr - 660π
Now, to find the maximum area, we can take the derivative of A with respect to r, set it equal to zero, and solve for r.
dA/dr = 6r + 8π + 30 - 66π = 0
Simplifying: 6r - 58π + 30 = 0
6r = 58π - 30
r = (58π - 30) / 6
r ≈ 29π/3 - 5
Therefore, to maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.
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How do you do this ??????????????????????
Answers
Answer:
b
Step-by-step explanation:
you can take the rectagel and you x the rectagel
a bag of assorted chocolates with 52 chocolates in total contains 12 dark chocolates and the rest are white chocolates. i draw a chocolate at random, consume it and then repeat the same process again, consuming 2 chocolates in total. what is the chance that both the chocolates that i consumed were dark?
Answers
Answer:
Step-by-step explanation:
After taking out the 12 dark chocolates, the bag now contains 52 - 12 = 40 white chocolates.
The probability of drawing a dark chocolate on the first draw is 12/52.
After the first chocolate is consumed, there are now 51 chocolates remaining in the bag, including 11 dark chocolates and 40 white chocolates.
The probability of drawing a dark chocolate on the second draw, given that a dark chocolate was already consumed on the first draw, is 11/51.
The probability of drawing 2 dark chocolates in a row is the product of the probabilities of drawing a dark chocolate on the first and second draws:
(12/52) * (11/51) = 0.0597, or approximately 5.97%.
Therefore, the chance that both chocolates consumed were dark is approximately 5.97%.
Danielle takes her dog to be groomed. The fee to groom the dog is $75.00
plus 6.75% tax. Is $80.00 enough to pay for the service including tax? Justify
your answer. Pleaseeee helppp thank you!!
Answers
Answer:
no, it won't be enough because you would need $80.06
Step-by-step explanation:
I just found 6.75% of 75 and added it on
Nance is riding her bike to a friends house 4 and 1/2 miles away. She’s riding2 and 3/5 miles. How much farther does she need to ride.
Answers
Answer:
1 4/5 miles :)
Step-by-step explanation:
We first need to get them at a common denominator :)
4 1/2 = 4 5/10
2 3/5 = 2 6/10
Now we subtract :)
4 5/10 = 3 14/10
3 14/10 - 2 6/10 = 1 8/10 = 1 4/5
Have an amazing day!!
Please rate and mark brainliest!!
Nance still needs to ride 1 and 9/10 miles to reach her friend's house.
What is speed?Speed is a measure of how quickly an object moves from one place to another. It is defined as the distance traveled by an object per unit of time, and is often represented by the symbol "v". The formula for speed is:
Speed = Distance/Time
Nance is riding her bike to a friend's house that is 4 and 1/2 miles away. She has already ridden 2 and 3/5 miles. To find out how much farther she needs to ride, we can subtract the distance she has already ridden from the total distance:
Total distance = 4 and 1/2 miles
Distance already ridden = 2 and 3/5 miles
Total distance - Distance already ridden
4 and 1/2 - 2 and 3/5 = 9/2 - 13/5 (we need to get a common denominator)
= (45/10) - (26/10)
= 19/10
Therefore, Nance still needs to ride 1 and 9/10 miles to reach her friend's house.
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Evaluate the expression below when x = 9 and y = 12.
4(x + 6) - 3(y + 4)
Answers
how would i solve these equations 9x+y=16Y=7x
Answers
Starting from the given system of equations:
\(\begin{gathered} 9x+y=16 \\ y=7x \end{gathered}\)Since the variable y is already isolated in the second equation, we can use the substitution method to solve the system.
Replace y by 7x on the first equation:
\(\begin{gathered} 9x+y=16 \\ \Rightarrow9x+7x=16 \\ \Rightarrow16x=16 \\ \Rightarrow x=1 \end{gathered}\)Then. substitute the value x=1 back into the second equation to find the value of y:
\(\begin{gathered} y=7x \\ \Rightarrow y=7(1) \\ \Rightarrow y=7 \end{gathered}\)Therefore, the solution for this system of equations is:
\(\begin{gathered} x=1 \\ y=7 \end{gathered}\)8. The average height of a 3-year old girl is 38
inches, and the average growth rate per
year is 2.5 inches. Write an equation in
point-slope form that describes the height
of a girl y based on her age x.
SISISISIBIS
Answers
The equation is y = 2.5x+38 using slope form.
What is the slope of the line?Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
So, we know that formula two find the slope of the line joining two points which is:
The average height of a 3-year-old girl is 38 inches.The growth rate per year is 2.5 inches.So y = MX +c.
m is the slope and c is the constant intersect.
So the equation will be y = 2.5 x + 38.Hence the equation of the age will be y = 2.5x + 38.Therefore, the equation is y = 2.5x+38 using slope form.
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In the cafeteria, there is one large 10-seat table and many smaller 5-seat tables. There are enough tables to fit 200 students. Write an inequality and solve the possible number of 5-seat tables in the cafeteria. upload the paper work plz
Answers
PLZ HELP!!!!
Peter is saving to buy a new camera. The camera costs $50. Peter has already saved $23.25. His plan is to save $4.50 every week to save at least enough for the camera.
Write an inequality to model this situation.
How many weeks will it take Peter to save at least enough to buy the camera? Show your work.
Answers
if he saves money for 5 weeks he’ll have enough money
23.25+4(6)=50.12
Consider the statements and select the correct option below.
(a) cos(x) = 1-sin(x)/(cos(x)+cot(x))
(b) sin(x) = 1-cos(x)/(sec(x)+tan(x))
1. Only (a) is true
2. Only (b) is true
3. Both (a) and (b) are true
4. Neither (a) nor (b) are true
Answers
Option- 3 is correct that is both a and b are true.
a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)
b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)
Given that,
a. We have to prove the statement is true or false.
Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)
Now, Take the right hand side
= \(1 - \frac{sinx}{cscx+cotx}\)
= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)
By using LCM
= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)
= \(1 - \frac{sinx\times sinx}{1+cosx} }\)
= \(1 - \frac{sin^2x}{1+cosx} }\)
= \(\frac{1+cosx - sin^2x}{1+cosx} }\)
We know from trigonometric identities 1 - sin²x = cos²x
= \(\frac{cos^2x+cosx }{1+cosx} }\)
= \(\frac{cosx(1+cosx )}{1+cosx} }\)
= cosx
LHS = RHS
Therefore, The statement is true
b. We have to prove the statement is true or false.
Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)
Now, Take the right hand side
= \(1 - \frac{cosx}{secx+tanx}\)
= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)
By using LCM
= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)
= \(1 - \frac{cosx\times cosx}{1+sinx} }\)
= \(1 - \frac{cos^2x}{1+sinx} }\)
= \(\frac{1+sinx - cos^2x}{1+sinx} }\)
We know from trigonometric identities 1 - cos²x = sin²x
= \(\frac{sin^2x+sinx }{1+sinx} }\)
= \(\frac{cosx(1+sinx )}{1+sinx} }\)
= sinx
LHS = RHS
Therefore, The statement is true
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Hey, i need help with this simple geometry question. thanks!
Answers
The length of sides BC and XC in the triangle are 8.66 and 10 units respectively
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.
From the triangle shown, using trigonometric ratio:
sin(30) = 5/XC
XC = 10
Also:
tan(30) = 5/BC
BC = 8.66
The length of BC and XC are 8.66 and 10 units respectively
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help me for brainliest answer
Answers
Answer:
\(6n - 5\)
Step-by-step explanation:
\(7 - 1 = 6\)
\(6n - 5\)
to check whether your answer is correct.
\(n = 1 \\ 6 \times 1 - 5 \\ 6 - 5 \\ = 1\)
\(n = 2 \\ 6 \times 2 - 5 \\ 12 - 5 \\ = 7\)
yes, it's correct
hope this helps you
What is the length of CD?
If the perimeter of triangle ABC is 27.6 cm, what is the perimeter, in centimeters, of triangle BCD?
Answers
The length of CD is 3.75 cm and perimeter of BCD = 15.4 cm
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
AC = 27.6- (9.6+6)
AC = 27.6 - 15.6
AC = 9ncm
6/DC = 9.6/6
9.6 DC = 36
DC = 36/9.6
DC = 3.75 cm
BD/9 = 6/9.6
9.6BD = 54
BD = 54/9.6
BD = 5.6
perimeter = 5.6 + 3.75+ 6
= 15.4 cm
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-5x + 30 = -10 find the value of x using step by step equation.
Answers
-30=-30
-5x=-40
/-5 =/-5
X= 8
What is the value of x?
A.15 start root 3 end root
B.Start Fraction 15 over 2 End Fraction
C.5 start root 3 end root
D.Start Fraction 15 Start Root 2 End Root over 2 End Fraction
Answers
Answer:
5 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 30 = x/15
15 tan 30 = x
15 ( sqrt(3)/3) = x
5 sqrt(3) =x
Verify the trig identity: tan^2 theta + cot^2 theta / csc^2 theta = sec^2 theta
Answers
Answer:
See proof below
Step-by-step explanation:
In trigonometry identity
tan^2 theta = sin^2 theta /cos^2 theta
cot^2 theta = cos^2 theta/sin^2 theta
csc^2 theta = 1/sin^2 theta
Substitute into the expression
(sin^2 theta /cos^2 theta )+ (cos^2 theta/sin^2 theta)/1/sin^2 theta
= [sin^4theta + cos^4theta/cos^2 theta sin^2 theta]÷(1/sin^2 theta)
= 1/cos^2 theta sin^2 theta÷(1/sin^2 theta)
= 1/cos^2 theta sin^2 theta * sin^2 theta/1
= 1/cos^2theta
= sec^2theta (Proved!)
i need help with this worksheet, its due on sunday 1/16/2022
Answers
Answer:
See attached
Step-by-step explanation:
Hopefully you can read it okay, the graphs were quite small.
-> I cannot answer the last three accurately
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
random samples of size 16 are taken from an infinite population whose mean and standard deviation are 260 and 16, respectively. the distribution of the population is unknown. find the mean and the standard error of the mean.
Answers
By using the concept of statistics mean of sample distribution is 260 and standard deviation is 4
The practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample. is called as statistics.
More Importantly ,Statistics is used to do calculations of huge data distributed in some ways.
We have mean of infinite population. Mean of random sample will be also 260.
Now talking about standard error of the mean ,
we know very well that standard error of mean=standard deviation/\(\sqrt{x}\)
where x is size
We know that sample size is 16
Therefore standard error of mean is =16/\(\sqrt{16}\)=16/4=4
Hence mean of random sample is 260 and standard error of mean is 4
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2 3/5 times 3 1/3
Just answer please
Answers
Answer:
8
Step-by-step explanation:
Answer: 8.66666666667
Step-by-step explanation:
minimal sedation is defined as which of the following? group of answer choices less than 50% n2o in the second stage in the continuum more than 50% n2o in the second stage in the continuum less than 50% n2o in the first stage in the continuum more than 50% n2o in the first stage in the continuum
Answers
Minimal sedation is characterized by c) less than 50% N2O in the first stage of the continuum.
Minimal sedation is defined as a state in which the patient is able to respond normally to verbal commands, breathe on their own and maintain stable blood pressure and heart rate. It is achieved by administering a small dose of a sedative or anxiolytic medication.
Minimal sedation is a light form of sedation that allows the patient to remain conscious and responsive throughout the procedure, and it helps the patient to relax and reduce anxiety.
It is considered a safer option than deeper forms of sedation as the patient remains able to breathe on their own, which reduces the risk of complications. This level of sedation is often used in procedures such as dental work, minor skin procedures, and diagnostic tests.
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Of the students at Milton Middle School, 170 are girls. If 50% of the students are girls, how many total students are there at Milton Middle school?
Answers
The solution is :
There are 240 students in the school.
Here, we have,
Givens
55% of the total number of students in a school are girls.
Equation
55/100 * x = 132
Solution
Multiply both sides of the equation by 100
55/100x * 100 = 132 * 100
55x = 13200 [ Divide by 55 ]
55x/55 = 13200/55
x = 240
Hence, The solution is :
There are 240 students in the school.
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complete question:
Of the students at milton middle school, 132 are girls. if 55% of the students are girls, how many total students are there at milton middle school?
You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets. Your friend finds $1 near your table and asks if it belongs with the ticket money. Do you think it does?
Answers
The 1 dollars found near the table by your friend is likely the money for the tickets.
How to find if the money belong to the ticket money?You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets.
let
x = number of individual ticket
y = number of couple tickets = 2x
Therefore, using equation,
2x(10) + 6x = 1075
2x + x = 195
Hence,
20x + 6x = 1075
3x = 195
x = 195 / 3
x = 65
Hence,
26x = 1075
26(65) = 1690
Therefore, the money on the table is the ticket money because the money is short of the amount of the tickets in dollars.
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Three orders are placed at a sandwich shop. Four sandwiches, two beverages, and
one salad costs $40; two sandwiches, one beverage, and two salads costs $26; and
three sandwiches, three beverages, and two salads costs $38. How much does each
item cost?
Answers
The respective prices are given below as
The price of the sandwich is 20/3 dollars.
The salad may be purchased for a price of $16/3.
There is a fee of $2 for the drinks.
How can you build equations that are simultaneous?Let's say that the price of the sandwich is x.
Allow the price of salad to equal y.
Allow the price of drinks to equal z.
The new total for this meal is $46. It includes three sandwiches, three beers, and two salads. Thus;
3x + 3y + 2z = 40 ——- (eq 1)
The price of $29 covers two sandwiches, two drinks, and one salad.
Thus;
2x + 2y + z = 26 ——-(eq 2)
It will cost you $54 for four sandwiches, one drinks, and three salads. Thus;
4x + y + 3z = 38 ———-(eq 3)
The following are the results of concurrently solving the three equations:
x = 20/3
y = 16/3
z = 2
Therefore, the following is how much each item costs:
There is a charge of $20/3 for the sandwich.
The salad may be purchased for a price of $ 16/3.
There is a fee of $2 for the drinks.
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HELP WILL MARK AS BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Sandy bought a car for $17,500. Her monthly car payment is $346. The first month the amount applied to the principal is $283 and the interest amount is $63 Assume that each month the amount applied to the principal increases by $1 and the interest amount decrease by $1 Which spreadsheet shows the amount of interest she paid in the six months?
Answers
Answer:
I'm not quite sure how to point to which graph exactly, but I will tell you that it is the one that principal increases by one for six months, and interest decreases. It has "Month, Principal, Interest, and Total" written across the top in bold. Down the left-hand side, it has numbers 1-6. On the bottom, the first total is $363, and the second is $2076.
Step-by-step explanation:
There is very limited math involved in this question. The first step is to find a graph where each month, the principal number increases by one dollar and the interest decreases by one dollar. This should go on for six months. We can now eliminate two graphs. For a third, you must remember that the interest starts in the sixty, and the principal payment is in the two hundred eighties. By now, we have our graph. The final step to double-check this is to add up the total interest and principal (which should be on the side). All totals should be $346 as we're basically just trading one number for another (-1+1). You should also go to the bottom and fill in the blank in the principal column. In this box, you should put the total of all principals together.
Hope this helps!
CenterWare is a manufacturer of large flower pots for urban settings. The company has these standards: Read the requirements Requirement 1. Compute the direct labor rate variance and the direct labor efficiency variance. (Enter the variances as positive numbers, Enter favorable (F) or unfavorable (U), Abbreviations used: DL = Direct labor) Begin with the direct labor rate variance. First determine the formula for the rate variance, then compute the rate variance for direct labor DL rate variance Х Standard Price and Volume Co hou flor Dir Dir Act ove Direct materials (resin). Direct labor..... Standard variable manufacturing overhead rate Budgeted fixed manufacturing overhead. Standard fixed MOH rate 10 pounds per pot at a cost of $5.00 per pound 2.0 hours at a cost of $21.00 per hour .$3.00 per direct labor hour $16.000 $10.00 per direct labor hour (DLH) Act Stal ove pro Print Done e i Actual Results - X Center Ware allocated fixed manufacturing overhead to production based on standard direct labor hours. Last month, the company reported the following actual results for the production of 1,000 flower pots: Purchased 11.400 pounds at a cost of $5.10 per pound; Direct materials... used 10,700 pounds to produce 1,000 pots Worked 2.5 hours per flower pot (2,500 total DLH) at a Direct labor cost of $18.00 per hour Actual variable manufacturing $3.40 per direct labor hour for total actual variable overhead manufacturing overhead of $8,500 Actual fixed manufacturing overhead $15.700 Standard fixed manufacturing overhead allocated based on actual production.. $20,000 1. Compute the direct labor rate variance and the direct labor efficiency variance. 2. What is the total variance for direct labor? 3. Who is generally responsible for each variance? 4. Interpret the variances.
Answers
CenterWare's direct labor rate variance is $2,100 unfavorable, indicating that the actual rate paid for labor was higher than the standard rate. The direct labor efficiency variance is $2,500 favorable, suggesting that the company achieved higher productivity than expected. The total variance for direct labor is $400 favorable.
To compute the direct labor rate variance, we need to calculate the difference between the actual rate and the standard rate, and then multiply it by the actual hours worked. The formula for the rate variance is (Actual Rate - Standard Rate) × Actual Hours. In this case, the standard rate is $21.00 per hour, and the actual rate is $18.00 per hour. The actual hours worked are 2,500 DLH. Plugging in these values, we find the direct labor rate variance to be ($18.00 - $21.00) × 2,500 = -$7,500, indicating an unfavourable variance.
To calculate the direct labor efficiency variance, we need to find the difference between the actual hours worked and the standard hours allowed, and then multiply it by the standard rate. The formula for the efficiency variance is (Actual Hours - Standard Hours) × Standard Rate. The standard hours allowed are 2,000 DLH (1,000 pots × 2.0 hours per pot). Substituting the values, we get (2,500 - 2,000) × $21.00 = $10,500, indicating a favorable variance.
The total variance for direct labor is the sum of the rate variance and the efficiency variance. In this case, the total variance is -$7,500 + $10,500 = $3,000, which is favorable, indicating that the company performed better than expected in terms of labor cost and efficiency.
The responsibility for the rate variance generally lies with the purchasing department, as they are responsible for negotiating labor rates and purchasing materials at the standard price. The efficiency variance is typically the responsibility of the production department, as they are accountable for achieving the standard labor hours and maximizing productivity.
The rate variance reflects the difference between the actual rate paid for labor and the standard rate. An unfavorable rate variance suggests that the company paid more for labor than anticipated, which could be due to factors like higher wages or inefficient labor management. Conversely, a favorable rate variance would indicate cost savings in labor.
The efficiency variance measures the productivity of labor and represents the difference between the actual hours worked and the standard hours allowed. A favorable efficiency variance implies that the company achieved higher productivity or used fewer labor hours than expected. It could result from factors such as skilled and efficient labor, improved production processes, or effective workforce management.
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