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Suppose that the cost function for a product is given by C(x) =.002^3 -9x + 4000.
Find the production level that will produce the minimum average cost per unit.

2007-10-07 14:06:03 · 1 answers · asked by Doug 1 in Science & Mathematics Mathematics

Could you explain and show work so I can understand better?

2007-10-08 12:03:42 · update #1

1 answers

Minimum and maximum values always occur where the derivative is zero.

Your C(x) is a cubic so its derivative is a quadratic. A quadratic has at most two zeros, and there is a simple formula to find them.

So compute the derivative; find its roots; and then check which, if any, of them are for a minimum of C.

All this assumes that C(x) is the average cost per unit when producing x units. If not, adjust accordingly.

2007-10-07 15:54:31 · answer #1 · answered by simplicitus 7 · 0 0

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