Production: In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on...

Production: In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point

with n measured in thousands of units of input and T measured in thousands of units of product.

a. Make a graph of T as a function of n. Include values of n up to 1.5 thousand units.

 b. Express using functional notation the amount produced if the input is 1.45 thousand units, and then calculate that value.

 c. Find the approximate location of the inflection point and explain what it means in practical terms.

 d. What is the maximum amount produced?