Blog 4 Miles VB

Hello class! I know many of you are business majors, hence why you took this course. For all this math to be useful to you, it has to applied. Revenue and profit functions are great examples of how math is useful for the business world. 

I know that the difference between revenue and profit is obvious for most of you, but it is important to understand that profit is the piece of the revenue that is left behind after costs are subtracted.

So to apply derivatives and calculus, we will be finding the marginal revenue and profit. That means the revenue or profit derived from making/selling one more unit.

So lets say someone is selling oregano. She decides that the demand function for her oregano is p=1000/√x per ounce. 

So revenue is equal to the number of ounces she sells (x) times the price (p)

So now we have to find what this means in terms of MARGINAL revenue. To do this, we find the derivative of the revenue function. So for instance when x=100: 

This all means that the revenue from selling the 101st ounce of oregano is $50. Pretty handy stuff to know in the business world.

So now lets find the marginal profits. First lets find the profit function. Well, profit (p) is revenue minus costs as I said before. So we express that mathematically by subtracting our cost function from our revenue. Lets say our cost function is C(x)= 10x + 10√x + 10,000.

So now to find the marginal profit, we must find the derivative of it at x=100

So this means that when she sells the 101st ounce of oregano, her profit is $35. This is really quite simple once you understand what is happening. The marginal profit is simply the marginal revenue minus the marginal costs. In this situation, her costs may be growing the oregano. Hope you enjoyed this lesson and have a nice night!