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

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.

Let’s get the good stuff! Words, words, words! Let’s get the good stuff! Το μαθηματικό πρότυπο C( x ) = 200 x + 60000 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?

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

Plug and chug x items ~ 800 items Guess x = 800 c ( x ) = 200 x + 60000 This is a function c ( 800 ) = 200 ( 800 ) + 60000 Just plug in the value for x c ( 800 ) = 160000 + 60000 Chug along until you get it! c ( 800 ) = 220,000

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!

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.

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.

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.

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.

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

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!