SOLUTION: Good evening, i need home help. it is due today. thanks! Callaway Golf Company has determined that the cost, C, of manufacturing x golf clubs may be expressed by the quadractic

Algebra ->  Functions -> SOLUTION: Good evening, i need home help. it is due today. thanks! Callaway Golf Company has determined that the cost, C, of manufacturing x golf clubs may be expressed by the quadractic       Log On


   

Question 1112312: Good evening, i need home help. it is due today. thanks!
Callaway Golf Company has determined that the cost, C, of manufacturing x golf clubs may be expressed by the quadractic function: C(x)=4.9x^2-617.4x+19600
a) how many clubs should be manufactured to minimize the cost
b) at this level of production, what is the cost?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A quadratic function can be written in the form
f%28x%29=ax%5E2%2Bbx%2Bc ,
with constants a , b , and c and a%3E0 ,
and has a minimum at
x=%28-b%29%2Fa .
In the case of C%28x%29=4.9x%5E2-617.4x%2B19600 ,
a=4.9 , b=-617.4 and c=19600 ;
the minimum occurs at x=617.4%2F%282%2A4.9%29=617.4%2F9.8=highlight%2863%29 ,
and at that point the value of the function is
.

So, the minimum of C%28x%29 occurs at highlight%28x=63%29 , and is highlight%28C%2863%29=151.9%29 .

In reality, it does not make sense for C%28x%29=4.9x%5E2-617.4x%2B19600
to be the total cost of manufacturing x golf clubs.
It seems more believable that C%28x%29=4.9x%5E2-617.4x%2B19600 could be the cost per club to manufacture x golf clubs.