Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 8

The Accentuate Consulting Firm has eight projects for which it has contracted with clients to develop computer systems and software. The firm has 35 team members it can assign to the projects. The firm has developed the following profit functions for each project, where xi equals the number of team members assigned to a project:
These functions take into account the project completion time, cost, and probability of successful completion based on the number of team members assigned. The functions reflect the fact that profit increases but at a decreasing rate as team members are assigned. Thus, as additional team members are assigned to a project, the marginal effect decreases. Determine the optimal number of team members to assign to each project in order to maximize profit.