Adrian SImion- Blog Post 4                                                      April 20th 2015 

Blog Post 4=  The Average Cost

          Good afternoon students of American University! First I would like to thank you all for signing up for my course. I promise that this semester will be a fun math journey you will all enjoy. I plan to teach mathematics in a fun and exciting way that all student can have the experience of enjoying. I am professor Adrian Simion, but you can all call me by my first name, Adrian. This will make me feel younger haha, I am just joking. Today we will start one of my favorite lessons in Applied Calculus. I will be teaching all of you how to find the Average cost of a quantity. 

          Now you may ask, What is an Average cost? Well look no further! The explanation is here and clear! Average cost can be defined as the cost per unit of a quantity. The average cost also has a formula that we can use to find an exact number for each quantity. 

                            The formula can be written out as:   a(q)=C(q)/q

           Now students don't freak out when you see this formula. I will explain it from left to right so that you can have a better understanding of what each part means. So to translate the formula into words, it means that the average cost equals the total cost of producing the quantity of that item divided by the number of units that have been produced. 

       So to find the average cost you must first figure out what the cost function of the said item is. Lets do an example with the cost function so that you can better understand how to reach the average cost. 

         So the formula of a cost function is written like this 

 Cost function = Variable cost + Fixed cost  

 Can also be written like this:C(x) = mx + b

           So lets use the example of finding the cost function of the Playstation 4. In honor of its release this year to the public market.  To start let us begin with saying that the cost function for producing playstation 4's is written as: 

                                         C(q)= 150(q)+10,000

       Allowing for q to represent the number of Playstation 4's that will be produced by the company.

       So let us say that we want to know the Cost to produce 80 Playstation 4's. We first start by plugging 80 for "Q". Which would look like this:

                                     

                                        C(q)=150(80)+10,000   = ???

        Now the next step is very simple. Once all is plugged into the equation all you have to do is solve it. So you would multiply 150 by 80 and then add 10,000 to the final solution. Giving you the answer of: $13,000 to produce 80 Playstation 4's.

                                      C((q)=150(80)+10,000   = $13,000

         So the cost of producing 80 Playstation 4's would be a whooping $13,000!!! That a lot of money isn't it boys and girls?

         Now on to the last step of finding the Average cost. C(q) was the last part that we needed to solve for the whole formula. After finding what C(q) equals we must now plug it in the Average cost formula. We start by writing the formula out.

                                       A(q)=C(q)/q

Now we plug in the cost function: 13,000 and divid it by the quantity: 80

               

                                       A(q)=13,000/80

After doing the required steps in the equation an answer should come forth:

                                       A(q)= $162.5 per Playstation 4

                   

      Now students I hope that this example was clear for all of you to understand how to find the average cost of an item. I am going to pass out a worksheet with some more example that you can work on over the weekend. Please spend time answering each of the questions carefully. If you get stuck on a problem or have any questions, please feel free to shoot me an email and ill get back to you as soon as possible. I will put these notes online so that you can use them to your advantage. 

     Remember that in this class we take tons of quizzes to make sure that each student is on track and understands the material provided to them. I will be quizzing you all on this when we come back from the weekend so i expect all A's!! Good luck to you all and ill see you on Monday. Enjoy your weekends and please everyone be safe!!