A private foundation has offered $3 million to allocate to cities to help fund programs that aid the homeless. Grant proposals were received from cities A, B, and C seeking assistance of $750,000, $1.2 million, and $2.5 million, respectively. In the grant proposals, cities were requested to quantify the number of assistance units that would be provided using the funds (an assistance unit is a night on a bed in a shelter or a free meal). Cities A, B, and C reported they could provide 485,000, 850,000, and 1.5 million assistance units, respectively, with the funds requested during the coming year. The directors of the foundation have two objectives. They want to maximize the number of assistance units obtained with the $3 million. However, they also want to help each of the cities by funding as much of their individual requests as possible (this might be done by maximizing the minimum percentage of funding received by any city).

a. Formulate an MOLP for this problem.

b. Determine the best possible value for each objective in the problem.

c. Implement your model in a spreadsheet and solve it to determine the solution that minimizes the maximum percentage deviation from the optimal objective function values. What solution do you obtain?