I'm having trouble getting the solution... please help!
Given a cost function of C= 11x^3 / 82944000 - 9x + 2200 / x^2 , what production level will minimize the cost per item?
thank you very much for your help!
2007-12-17 05:29:27 · 2 answers · asked by calchelp1 1 in Science & Mathematics ➔ Mathematics
Take the first derivative and set it equal to zero then solve for X.
2007-12-17 05:37:46 · answer #1 · answered by Tim C 7 · 0⤊ 0⤋
C= 11x^3 / 82944000 - 9x + 2200* x^-2
To find the production level for maximum cost you will need to find the derivative of the cost function, set it equal to zero and sove for x.
dC/dt = 33/82944000*x^2 - 9 -4400 * x^-1
Since the numbers do not lend themselve to an easy solution for x. I will solve for x with a graphing calculator. (A good investment.)
x = 4,983.98
(There is another negative solution that is not appropriate for the problem.)
To be complete, you should take the second derivative substitute to see if in fact you have a production for minimum cost, or substitute 4983.98, and a number near both greater and less than into the cost function, to see if you have minimum cost.
2007-12-17 05:50:33 · answer #2 · answered by Peter m 5 · 0⤊ 0⤋