Math Is Fun Forum

4littlepiggiesmom

Member

Registered: 2006-01-09

Posts: 42

Quadratic Function Word Problem???? Yikes!

A manufacturer has daily production costs of
C = 10,000- 10 x + o.0450(x Squared)
Where C is the total cost in dollars and X is the hunber of units produced. How many units should be produced each day to yield a minimum cost?

I got c= 9999.995 which would round to 10, 000 units? Any where close?

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,421

Re: Quadratic Function Word Problem???? Yikes!

C = 10,000 - 10x + 0.0450x²
dC/dx = -10 + 0.09x
d²c/dx² = 0.09
Put dC/dx = 0
- 10 + 0.09x = 0
0.09x = 10
x = 10/0.09
Substituting,
C = 10.000 - 100/0.09 + 0.0450(10/0.09)²
I am not too sure, maybe I went wrong somewhere

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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Quadratic Function Word Problem???? Yikes!

x = 10/0.09 = 111 units (rounded), as you said ganesh.

And C = 9444.445 per unit

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman