Task 2

Maximizing Production

 

Henry Ford has been called the Father of Industry with his use and development of the assembly‐line process of mass production. The field of Industrial Ecology views Ford’s approach to maximizing production to be reflective of how nature and man has developed to best use limited resources in a competitive setting.

1. It is estimated that a person learning a certain assembly‐line task takes T minutes to perform the task after x repetitions.

a‐ Use a graphing utility to graph T(x) with respect to x.

b‐ Find dT/dt if the change in repetitions per time (dx/dt) is 4, and 4 repetitions of the task have been performed.

 

 

 

 

 

 

 

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 2‐ The rate at which Ford’s factory produces cars is described by this function:

where C is cars produced and N is the factory’s limiting storage capacity of the parts.Let N =12. Show that the graph of C has at least one inflection point at C = N/2. (Use implicit differentiation.)