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**4littlepiggiesmom****Member**- Registered: 2006-01-09
- Posts: 42

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?

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,812

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: 7,631

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

And C = 9444.445 per unit

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

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