Quiz 5
Modeling with the Gradient




1) The production P of a factory can be represented by the function



where x is the number of workers (in hundreds) employed at the plant, and y is the amount of money invested (in millions). Currently, the company employs 1 unit of workers and 16 units of money.

a) What is the gradient of the production for x=1, y=16?

Solution

b) The company is thinking of increasing the units of money y invested, while cutting the number of workers x by the same amount. Using directional derivatives, describe the effect of this on production.

Solution

c) In which direction should the company move instead to get the largest increase in production?

Solution

d) What is the largest rate at which the production can grow, if we start with x=1, y=16?

Solution



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