Service planners for a regional health authority have been reviewing wait times for partial and full hip replacements. their analysis shows that the wait time for partial hip replacements is much longer than for full hip replacements, despite the fact that a full hip replacement is a longer, more complicated surgery. specifically, a full hip replacement requires three hours of operating room (or) time, whereas a partial hip replacement requires only two hours of or time. the regional health authority compensates surgeons twice as much for a full hip replacement as for a partial hip replacement. each surgeon is given no more than 20 hours of or time per week, and surgeons are free to choose how they book their time. the health authority wants to understand why the wait times for partial hip replacements are so much longer than the wait times for full hip replacements. develop a hypothesis as to why this occurs by completing the following analysis:
consider the allocation of or time from the surgeon’s perspective. develop a mathematical formulation of the problem by writing an expression for the surgeon’s compensation as determined by the type of surgeries performed and any constraints under which the surgeon operates. (15 marks)
using your answer from 3, determine the optimal allocation of or times between the two types of hip surgery as determined by the surgeon. what is the optimal allocation in terms of benefit to the greatest number of patients? what is the optimal allocation in terms of compensation for the surgeon? explain why your answer is the best strategy for optimization. (15 marks)
using what you have discovered in your analysis, propose a hypothesis as to why wait times for partial hip replacements are much longer than for full hip replacements. (10 marks)