Textbook Problem

Coach Night is trying to choose the starting lineup for the basketball team. The team consists of seven players who have been rated on a scale of 1 (poor) to 3 (excellent) according to their ball handling, shooting, rebounding, and defensive abilities. The positions that each player is allowed to play and the players’ abilities are listed in the file P06_43.xlsx. The five-player starting lineup must satisfy the following restrictions:

• At least four members must be able to play guard (G), at least two members must be able to play forward (F), and at least one member must be able to play center (C).
• The average ballhandling, shooting, and rebounding level of the starting lineup must each be at least 1.8.
• Either player 2 or player 3 (or both) must start. Given these constraints, Coach Night wants to maximize the total defensive ability of the starting team. Use Solver to determine his starting team.