SOLUTION: The cost in C dollars of manufacturing 'x' bicycles at Holliday's Production Plant is given by the function C(x) = 2x² - 800x + 92,000. Find the minimum cost.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The cost in C dollars of manufacturing 'x' bicycles at Holliday's Production Plant is given by the function C(x) = 2x² - 800x + 92,000. Find the minimum cost.      Log On


   



Question 953095: The cost in C dollars of manufacturing 'x' bicycles at Holliday's Production Plant is given by the function
C(x) = 2x² - 800x + 92,000.
Find the minimum cost.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+C%28x%29+=+2x%5E2+-+800x+%2B+92000+
+C%28x%29+=+x%5E2+-+400x+%2B+46000+
The minimum value of +x+%7C is
given by:
+x%5Bmin%5D+=+-b%2F%282a%29+
where:
The equation has the form:
+C%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+a+=+1+
+b+=+-400+
+x%5Bmin%5D+=+-%28-400%29%2F%282%2A1%29+
+x%5Bmin%5D+=+400%2F2+
+x%5Bmin%5D+=+200+
The minimum x is 200
------------------------
+C%28x%29+=+x%5E2+-+400x+%2B+46000+
+C%28200%29+=+200%5E2+-+400%2A200+%2B+46000+
+C%28200%29+=+40000+-+80000+%2B+46000+
+C%28200%29+=+-40000+%2B+46000+
+C%28200%29+=+6000+
The minimum cost is $6,000
-------------
Check:
Here's the plot:
+graph%28+400%2C+400%2C+-80%2C+400%2C+-5000%2C+50000%2C+x%5E2+-+400x+%2B+46000+%29+