Expert: Paul Klarreich - 10/21/2011

Question
A manufacturer finds that in producing x units per day (for 0<x<100), three different kinds of cost are involved:
(a) A fixed cost of $1,200 per day in wages
(b) A production cost of $1.20 per day for each unit produced
(c) An ordering cost of 100/x^2 dollars per day.
Express the total cost as a function of x and determine the level of production that results in minimal total cost.

Answer
Questioner:kristen
Country:Tennessee, United States
Category:Calculus
Private:No
Subject:Calculus applications of derivatives

Question:

A manufacturer finds that in producing x units per day (for 0<x<100), three different kinds of cost are involved:
(a) A fixed cost of $1,200 per day in wages
(b) A production cost of $1.20 per day for each unit produced
(c) An ordering cost of 100/x^2 dollars per day.
Express the total cost as a function of x and determine the level of production that results in minimal total cost.
................................................
Looks like it is just:

C = 1200 + 1.2x + 100/x^2

The rest is the usual max-min stuff.  Don't forget about the endpoints.
I assume you have looked at:

http://en.allexperts.com/q/Calculus-2063/2009/11/Maximum-minimum-problem-41.htm