Mathematical optimization

Mathematical optimization


The BU is a new professional basketball franchise in Massachusetts. The team’s general manager, Tony, and coach, Seth, are trying to develop a roster of players. Following table below provides past performance averages on the free agents : The signing of free agents to the team should meet the following restrictions: ➢ Sign at least four but no more than six free agents. ➢ The set of players signed should combine for at least 80 points per game on average, at least 40 rebounds per game on average, at least 25 assists per game on average. ➢ The average time a selected player should be able to play is at least 36 minutes per game. ➢ At most two players should be signed at the same position. ➢ If Player 7 is signed then either Player 6 or Player 10 must be signed as well. (a) Formulate an integer linear program that meets the stated requirements while minimizing the cost. (b) Use Excel Solver (or other software) to solve the model you created in part (a). (c) Suppose at most $50 million per year is available for these new players. Does the team have enough money to implement the solution you identified in part (b)? If not, reformulate the model to include a budget constraint and resolve. What do you observe and what do you suggest the team do?