aka Mathematical Models and Applications

Παρουσίαση με θέμα: "aka Mathematical Models and Applications"— Μεταγράφημα παρουσίασης:

1 aka Mathematical Models and Applications
Plug and Chug aka Mathematical Models and Applications

2 Is it all Greek to you? Blah, Blah, Blah!
The mathematical model C( x ) = 200x + 60,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this, how much does it cost to produce 800 items? Is it all Greek to you? Το μαθηματικό πρότυπο C( x ) = 200x + 60,000 που παρουσιάζεται εδώ αντιπροσωπεύει τις δαπάνες σε δολάρια που μια επιχείρηση έχει στην κατασκευή των στοιχείων Χ κατά τη διάρκεια ενός μήνα. Με βάση αυτό, πόσο αυτό κοστίζει για να παραγάγει 800 στοιχεία.

3 Let’s get the good stuff!
Words, words, words! Let’s get the good stuff! Το μαθηματικό πρότυπο C( x ) = 200 x που παρουσιάζεται εδώ αντιπροσωπεύει τις δαπάνες σε δολάρια που μια επιχείρηση έχει στην κατασκευή των στοιχείων x items κατά τη διάρκεια ενός μήνα. Με βάση αυτό, πόσο αυτό κοστίζει για να παραγάγει 800 items?

4 What does it mean? c ( x ) = 200 x + 60000 This is function notation
x items x seems to be the number of items 800 items? So the question ( ? ) is about when x = 800 items

5 Plug and chug x items ~ 800 items Guess x = 800
c ( x ) = 200 x This is a function c ( 800 ) = 200 ( 800 ) Just plug in the value for x c ( 800 ) = Chug along until you get it! c ( 800 ) = 220,000

6 Did we answer the question?
C( x ) = 200x + 60,000 represents the cost …(of)… manufacturing x items How much does it cost to produce 800 items? We found C( 800 ) so we found the cost of manufacturing 800 items!

7 What does it mean? Now that we are no longer scared of the problem, let’s pick it apart a little more. The model is showing cost C(x) as a function of the number of items manufactured. The more items that are made in a month, the higher the cost.

8 Independent and dependent variables
The number of items is an independent variable ( we could make 1 or we could make 800) The cost is dependent because it varies depending on the number of items produced.

9 What’s up with the 60,000? C( x ) = 200x + 60,000 represents the cost …(of)… manufacturing x items The 60,000 is a fixed cost – rent, utilities, etc. We have to pay that just to keep the building whether we make any items or not. The 200x is a variable cost. It cost us $200 in materials, labor, etc. to make each widget. The cost of the actual widgets is $200 times each one we make.

10 Total cost C( x ) = 200x + 60,000 represents the cost …(of)… manufacturing x items Our total cost is what we get when we add our fixed costs to our variable costs.

11 We did it! C( x ) = 200x + 60,000 represents the cost …(of)… manufacturing x items We found C( 800 ) so we found the total cost of manufacturing 800 items. 160,000 for the items themselves 60,000 for fixed costs 220,000 total cost

12 When you’re blinded by the words . . .
Look for the good stuff. Plug the values into the function. Chug along until you have an answer. Re-read the words to make sure you’ve answered the question!