A private foundation has offered $3.5 million and will use all of these funds 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 $3.5 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 proportion of funding received by any city). (Let

X₁

be the amount of funds received by City A in thousands of dollars, let

X₂

be the amount of funds received by City B in thousands of dollars, and let

X₃

be the amount of funds received by City C in thousands of dollars.)

Formulate a MOLP for this problem.

assistance units MAX:

minimum proportion funding MAX:

Q Subject to: total funds received (in thousands of dollars)

City A (funding request)

City B (funding request)

City C (funding request)

City A (minimum proportion of funding)

QCity B (minimum proportion of funding)

QCity C (minimum proportion of funding)

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

What is the maximum number of assistance units that be provided while satisfying the first four constraints? What is the maximum minimum proportion of funding that can be achieved while satisfying the first four constraints? (Round your answer to four decimal places.

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? (Round your answers to two decimal places.)

Please use values given in chart.