Monday, April 20, 2015
Blog 4: Average Cost
Hello! My name is Professor Bookter and today I will teach you about the average cost function. Looking at my roster, it seems lots of you are Kogod majors! This lesson will actually be beneficial to you in your business futures (I promise!). You use the average cost function when trying to determine cost per unite of producing a certain quantity. Basically, to find this, you will divide the total cost of a production by the number of units produced.
Let us call the cost of producing a quantity q is C(q). The average cost would be a(q). The number of quantity of items is q.
The equation you will use for finding the average cost is a(q)=C(q)/q.
Be careful not to confuse the average cost with the marginal cost! Both have the same units: dollars per item. Just be an eagle eye!
Let us look at an example.
Hunter (as in the company that sells Hunter rainboots) has a cost function C(q)=.01q^3-.6q^2+13q+1000 (in dollars), where q is the number of pairs of rainboots were produced. If 100 pairs of rainboots are produced, find the average cost per pair of rainboots.
The total cost of producing 100 pairs of rain boots is given by C(100)=.01(100)^3-.6(100)^2+13(100)+1000= $6300.
We find the average cost per pairs by dividing by 100, the number of pairs produced.
Average cost = 6300/100= 63 dollars per pair.
If 100 pairs of Hunter rain boots were produced, the average cost is $63 per case.
This is fairly self-explanatory. Use your notes to do your Think-pair-share. I will be walking around for questions! The sheets are up at the front!
Blog Post 4
Hi my
name is Matthias Ng, and I will be explaining the teaching Average Cost
Today,
we will be learning the concept of average cost. The concept of average cost
seems fairly self-explanatory. Average cost is simply the average cost of
producing a unit. Average cost differs from marginal cost (recall, marginal
cost is the cost of producing each additional unit), because it includes the
fixed costs. Average cost will take the fixed and variable cost into
consideration. First, fixed costs are costs that do not fluctuate and are
expenses that a company will pay regardless of future business activity, while
variable costs are costs that fluctuate based on production. Fixed cost and
variable cost add up to equal the total cost. To find the average cost, you
simply divide the total cost by the quantity of units.
average
cost = total cost
quantity of output
To
better understand this concept, let’s go through an example.
Let’s
say the Pink Panther Company has a fixed cost of $10,000 and the cost of
producing each unit cost the company a further $15. How would we find the average
cost of producing 100 units?
1. First, we would find the total
cost. We find this by multiplying 15 by 100. We multiple 15 by 100 because we
want to know how much it costs to produce 100 units and it costs $15 dollars
for every unit. We get $1,500 to produce 100 units. However, we are not done
computing the total costs, next we have to add the fixed costs, which is $10,000.
Therefore, the total cost of producing 100 units is $1,500 + $10,000 = $11,500
2. The next step, is to divide the
total cost by the quantity. So, $11,500 is divided by 100
$11,500/100 = $115 the average
cost of producing 100 units is $115
Lastly, its important to note that in comparison to the marginal
cost, the marginal cost will have a very consistent and gentle slope, while the
average cost will generally have a steeper slope, as the first few units will
be more expensive because it mitigates the initial costs of operating.
Eventually, the average costs will taper off and the graph will become less
steep. We also know that average cost is higher by just comparing it with the
marginal cost and it will move towards the marginal costs as the initial costs
are erased away after profits are realized.
Seth Brennock Blog Post 4
Howdy class,
My name is Professor Seth Brennock. I have studied under the great Venessa Little. Therefore I am more than qualified to teach math to you. Today we are going to learn about Profit and revenue functions.
Given that this is a applied calc class and may of you are business majors, I thought this would be a great lesson that you can apply to many of your business related courses.
First lets look at the cost function!
The cost function tells us the cost of C as a function of the # of items x. This meaning C(x) is the cost of x items and has the form:
Cost+Variable cost+ Fixed Cost
where the variable cost is a function of x and the fixed cost is constant, making the cost function look like:
C(x) = mx+b
This is called the linear coast function; where m= the marginal cost.
Got it? Great! Now lets look at the revenue function!
Revenue is the result of one or more business transactions accumulated total payment received. This can also be called gross profit.
R(x) is going to represent the revenue of selling x amount of items
The entire function is gonna look like:
R(x)= mx (m represents the marginal revenue)
When we put these together we can then find the Profit Function.
The profits is the net proceeds after you subtract the cost from the revenue.
The break even point is when you can the side equal each other, if you can from there increase revenue or decrease cost, profit will increase.
Now lets look at an example of this in practice:
A toy store must pay $10.25 each for a popular computer game. The store's fixed cost for this game is $1302. The store sells each one of these games for $15.50.
a) Write the cost function
b) write the revenue function
c) write the profit function
d) find the break-even quantity.
Answer:
a) Cost = fixed + variable costs
C = 1302 + 10.25x
where C = Cost and x = number of units
b) R = Price per unit *number of units.
R = 15.50x
c) Profit = Revenue - Cost
P = 15.50x - 1302 - 10.25x
P = 5.25x - 1302
d) Break-even quantity is the quantity at which cost = revenue or Profit = 0
P = 5.25x - 1302 = 0
x = 248
Thanks for learning today class!
Work Cited
http://www.zweigmedia.com/RealWorld/tutorialsf0/framesF2A.html
http://www.statistica.com.au/more_maths.html
Notes from class
Profit= Revenue- Cost
My name is Professor Seth Brennock. I have studied under the great Venessa Little. Therefore I am more than qualified to teach math to you. Today we are going to learn about Profit and revenue functions.
Given that this is a applied calc class and may of you are business majors, I thought this would be a great lesson that you can apply to many of your business related courses.
First lets look at the cost function!
The cost function tells us the cost of C as a function of the # of items x. This meaning C(x) is the cost of x items and has the form:
Cost+Variable cost+ Fixed Cost
where the variable cost is a function of x and the fixed cost is constant, making the cost function look like:
C(x) = mx+b
This is called the linear coast function; where m= the marginal cost.
Got it? Great! Now lets look at the revenue function!
Revenue is the result of one or more business transactions accumulated total payment received. This can also be called gross profit.
R(x) is going to represent the revenue of selling x amount of items
The entire function is gonna look like:
R(x)= mx (m represents the marginal revenue)
When we put these together we can then find the Profit Function.
The profits is the net proceeds after you subtract the cost from the revenue.
The break even point is when you can the side equal each other, if you can from there increase revenue or decrease cost, profit will increase.
Now lets look at an example of this in practice:
A toy store must pay $10.25 each for a popular computer game. The store's fixed cost for this game is $1302. The store sells each one of these games for $15.50.
a) Write the cost function
b) write the revenue function
c) write the profit function
d) find the break-even quantity.
Answer:
a) Cost = fixed + variable costs
C = 1302 + 10.25x
where C = Cost and x = number of units
b) R = Price per unit *number of units.
R = 15.50x
c) Profit = Revenue - Cost
P = 15.50x - 1302 - 10.25x
P = 5.25x - 1302
d) Break-even quantity is the quantity at which cost = revenue or Profit = 0
P = 5.25x - 1302 = 0
x = 248
Thanks for learning today class!
Work Cited
http://www.zweigmedia.com/RealWorld/tutorialsf0/framesF2A.html
http://www.statistica.com.au/more_maths.html
Notes from class
Profit= Revenue- Cost
Blog Post #4 Michael Dahlstrom
How to Find the Average Cost
By Michael Dahlstrom
Finding the Average Cost can be a little tricky, but if you follow the steps listed below you should be able to get a quick and correct answer every time! Here's how to do it:
1) In order to find the average cost, you need to plug your information into the formula:
A(q)= C(q)/(q)
In other words, the formula is the Average cost = the cost of each unit divided by the total amount of units.
2) We also will need to find the cost function, which is the formula:
Y = mx + b.
In other words, the total cost = variable cost per unit times the total units added to the fixed cost.
EXAMPLE
If I have a store that sells stuffed animals. If I produce 100 stuffed animals, and the total cost to produce the stuffed animals was $4 each, and a cost of the factory costing $200, then our cost formula would look like this:
Y = 4(100)+200
Based on the information, our total cost = $600. Now we can find the average cost...
A(q) = 600/100
Therefore, our average cost for every stuffed animal produced in $6.
If you have any additional questions, please feel free to email me at md2415a@student.american.edu
I hope that you can use this information to apply it to your own problem and remember to plug the information in the right places!
Good luck,
MICHAEL DAHLSTROM
By Michael Dahlstrom
Finding the Average Cost can be a little tricky, but if you follow the steps listed below you should be able to get a quick and correct answer every time! Here's how to do it:
1) In order to find the average cost, you need to plug your information into the formula:
A(q)= C(q)/(q)
In other words, the formula is the Average cost = the cost of each unit divided by the total amount of units.
2) We also will need to find the cost function, which is the formula:
Y = mx + b.
In other words, the total cost = variable cost per unit times the total units added to the fixed cost.
EXAMPLE
If I have a store that sells stuffed animals. If I produce 100 stuffed animals, and the total cost to produce the stuffed animals was $4 each, and a cost of the factory costing $200, then our cost formula would look like this:
Y = 4(100)+200
Based on the information, our total cost = $600. Now we can find the average cost...
A(q) = 600/100
Therefore, our average cost for every stuffed animal produced in $6.
If you have any additional questions, please feel free to email me at md2415a@student.american.edu
I hope that you can use this information to apply it to your own problem and remember to plug the information in the right places!
Good luck,
MICHAEL DAHLSTROM
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