Chapter 5.1, Problem 90E

Labor costs. If the rate of labor use in Problem 89 is

     $L\prime \left(x\right)=2,000x^{-1/3}$

and if the first 8 control units require 12,000 labor-hours, how many labor-hours, L(x), will be required for the first x control units? The first 27 control units?

89.    Labor costs. A defense contractor is starting production on a new missile control system. On the basis of data collected during the assembly of the first 16 control systems, the production manager obtained the following function describing the rate of labor use:

     $L\prime \left(x\right)=2,400x^{-1}{}^{/2}$

For example, after assembly of 16 units, the rate of assembly is 600 labor-hours per unit, and after assembly of 25 units, the rate of assembly is 480 labor-hours per unit. The more units assembled, the more efficient the process. If 19,200 labor-hours are required to assemble the first 16 units, how many labor-hours L(x) will be required to assemble the first x units? The first 25 units?