An operations manager is interested in modeling E(y), the expected length of time per month (in hours) that a machine will be shut down for repairs, as a function of the type of machine (001 or 002) and the age of the machine (in years).

a. Write a complete second-order model for machine downtime (y) as a function of age and machine type.

b. Give the reduced model required to determine whether the second-order terms in the model are necessary.

c. Give the reduced model required to determine whether the machine-type terms are necessary.