A town mayor received $4 million from the county for his programs and projects. The mayor discussed with the council how to allocate the funds and they decided to give the money to four ongoing programs: A workforce development program, a technology infrastructure project, a sustainability project, and a library. The mayor did not tell the councilors that he wants to distribute the money to projects according to what will make him look favorable to voters. He consulted his personal staff and they estimated the number of votes he will get per dollar spent on the four projects identified by the council. Program/Project Votes/dollar Workforce development 0.02 Technology infrastructure 0.09 Sustainability 0.06 Library 0.04 His staff also reminded the mayor that there are certain very wealthy and influential citizens who financed the last election who are expecting him to observe certain guidelines when allocating resources: 1. None of the programs can receive more than 40% of the total allocation. 2. The amount allocated to technology infrastructure cannot exceed the total allocated to both the sustainability project and the library. 3. The amount allocated to workforce development must at least equal the amount spent on the sustainability project. Any money not spent in the town will be returned to the government. The mayor wants to spend all he money to maximize the budget allocation. The mayor wants to know how much to allocate to each Drogram to maximize his votes 1. Formulate a linear programming model for this problem. 2. Solve the model by using the computer. 3. Discuss your recommendation. A town mayor received $4 million from the county for his programs and projects. The mayor discussed with the council how to allocate the funds and they decided to give the money to four ongoing programs: A workforce development program, a technology infrastructure project, a sustainability project, and a library. The mayor did not tell the councilors that he wants to distribute the money to projects according to what will make him look favorable to voters. He consulted his personal staff and they estimated the number of votes he will get per dollar spent on the four projects identified by the council. Program/Project Votes/dollar Workforce development 0.02 Technology infrastructure 0.09 Sustainability 0.06 Library 0.04 His staff also reminded the mayor that there are certain very wealthy and influential citizens who financed the last election who are expecting him to observe certain guidelines when allocating resources: 1. None of the programs can receive more than 40% of the total allocation. 2. The amount allocated to technology infrastructure cannot exceed the total allocated to both the sustainability project and the library. 3. The amount allocated to workforce development must at least equal the amount spent on the sustainability project. Any money not spent in the town will be returned to the government. The mayor wants to spend all he money to maximize the budget allocation. The mayor wants to know how much to allocate to each Drogram to maximize his votes 1. Formulate a linear programming model for this problem. 2. Solve the model by using the computer. 3. Discuss your recommendation
