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