SOLUTION: A cost function is given as {{{C(x)=(1/2)x^3-8x^2-80x+200}}}. Find the cost of producing 100 boxes

Algebra ->  Graphs -> SOLUTION: A cost function is given as {{{C(x)=(1/2)x^3-8x^2-80x+200}}}. Find the cost of producing 100 boxes      Log On


   

Question 138685: A cost function is given as C%28x%29=%281%2F2%29x%5E3-8x%5E2-80x%2B200. Find the cost of producing 100 boxes
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we're trying to find C%28100%29, our test zero is 100


Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.
100| 1/2 -8-80200
|



Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
100| 1/2 -8-80200
|
1/2




Multiply 100 by 1/2 and place the product (which is 50) right underneath the second coefficient (which is -8)
100| 1/2 -8-80200
| 50
1/2



Add 50 and -8 to get 42. Place the sum right underneath 50.
100| 1/2 -8-80200
| 50
1/2 42




Multiply 100 by 42 and place the product (which is 4200) right underneath the third coefficient (which is -80)
100| 1/2 -8-80200
| 50 4200
1/2 42 4120




Add 4200 and -80 to get 4120. Place the sum right underneath 4200.
100| 1/2 -8-80200
| 50 4200
1/2 42 4120




Multiply 100 by 4120 and place the product (which is 412000) right underneath the fourth coefficient (which is 200)
100| 1/2 -8-80200
| 50 4200 412000
1 42 4120




Add 412000 and 200 to get 412200. Place the sum right underneath 412000.
100| 1/2 -8-80200
| 50 4200 412000
1/2 42 4120 412200





Since the last column adds to 412200, we have a remainder of 412200.



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Answer:

So according to the remainder theorem, C%28100%29=412200


So the cost to produce 100 boxes is $412,200