The HAL computer must determine which of eight research and development (R&D) projects to undertake.

For each project, four quantities are of interest: (1) the net present value (NPV, in millions of dollars) of the project; (2) the annual growth rate in sales generated by the project; (3) the probability that the project will succeed; and (4) the cost (in millions of dollars) of the project. The relevant information is given in the file P16_16.xlsx. HAL has set the following four goals:

■ Goal 1: The total NPV of all chosen projects should be at least $200 million.

■ Goal 2: The average probability of success for all projects chosen should be at least 0.75.

■ Goal 3: The average growth rate of all projects chosen should be at least 15%.

■ Goal 4: The total cost of all chosen projects should be at most $1 billion.

For the following sets of priorities, use (integer) goal programming to determine the projects that should be selected.

a. Goal 2, Goal 4, Goal 1, Goal 3.

b. Goal 1, Goal 3, Goal 4, Goal 2.