non-profit org

Project Description:

beth dale is the director of development for a nonprofit organization that depends largely on charitable gifts for its operations. beth needs to assign four different staff people to make trips to call on four possible donors. only one staff person can call on each donor and each staff person can make only one call. beth estimates the probability of each staff person successfully obtaining the donation from each potential giver as follows:
donor
staff 1 2 3 4
sam 0.95 0.91 0.9 0.88
billie 0.92 0.95 0.95 0.82
sally 0.95 0.93 0.93 0.85
fred 0.94 0.87 0.92 0.86

a. formulate an nlp model to determine the task of staff persons to donors that maximizes the probability of receiving all donations.
b. implement your model in a spreadsheet and solve it. what is the optimal solution?
c. suppose it is estimated that the donations possible from donors 1,2, 3, and 4 are for $1m, $2m, $0.5m, and $0.75m respectively. how should beth assign her staff if she wants to maximize the expected value of the donations received?
d. all staffers will have the least luck soliciting funds from donor number 4, so no one really wants to be assigned to this donor. indeed, each staffer will regret not being assigned to the donor with whom they have the highest probability of success. suppose we define the amount of this regret for each staffer by their maximum probability of success minus the probability of success for their actual task. what task of staffers to donors will minimize the maximum regret suffered by any staffer?
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