30 Apr Question: Kindly do it in written form on word 2 Optimal Restructuring of Team Size (40 marks) There are cu…
kindly do it in written form on word
2 Optimal Restructuring of Team Size (40 marks)
There are currently three teams (labeled as X, Y, and Z) currently operating in a department. After a successful recruitment cycle, the manager of the department decides to do a re-organisation of the team structure with the aim to maximise overall productivity. Let x, y, and z denote the change of size of teams X, Y, and Z, respectively.2 Let the overall change of productivity of the department be given by
−2×2 + 4x − y 2 − 2y − 0.5z2 + z
1. Suppose the manager cannot change the size of team Z (i.e., z = 0). Present a graph that visualises how the overall change in productivity of the department changes with the change of size in teams X and Y. Comment on the relationship. [10 marks]
2. Use Solver to find the optimal change to the size of teams X, Y, and Z, if the department had hired exactly
(a) one new staff member
(b) fifteen new staff members
Based on your results comment on whether the manager would prefer to hire one or fifteen new members. Provide some intuition for your answer using the properties of the objective function. [30 marks]
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