Every year, the United States Congress must approve a budget for the coun- try. In order to be approved, the budget must get a majority of the votes in the Senate, a majority of votes in the House, and the signature of the President.

Most of the budget is easy to agree on - everyone supports things like basic operating expenses for the government, diplomats in foreign countries, and the armed forces; emergency relief funds in case of earthquakes, hurri- canes, etc.; maintenance of the interstate highway system; and so on. Other aspects of the budget, however, are less easy to agree on. For example, should there be a tax cut? Should the government spend money on de- fense research? Should they use some of the budget surplus to solidify social security? To pay off the debt to the United Nations? To give aid to farm- ers unable to make a living due to low food prices? Because of monetary restrictions, the budget can have money allocated for at most 4 of the 5 issues.

One Senator has asked his staff to categorize all of Congress (Senators and members of the House), as well as the President, by their views on the five controversial issues. The Senator's staff has compiled the following table. In order for a particular group to vote for a budget proposal, the proposal must allocate money in agreement with the group's views on more than half of the issues that the group cares about. For example, the Senate Group 2 only cares about 3 of the issues. Therefore, any budget proposal that agrees with their views on at least two out of the three issues they care about (allocating money for a Tax Cut and Defense Research, but not for the United Nations) would get their 16 votes in the Senate. So a budget proposal that funds Tax Cuts, Defense Research, Social Security and United Nations would get the group's votes. In order to be approved, a budget must get a majority of the votes (at least 51 out of 100) in the Senate, a majority of the votes (at least 218 out of 435) in the House of Representatives,andthe approval of the President.

Formulate a decision model that the Senator could use to devise a budget proposal that would be approved by all three (Senate, House, and President) while funding as many budgetary issues as possible. Specify your decision variables, objective function, and constraints clearly. Build a spreadsheet model and report the optimal solution and include a copy of the spread- sheet model along with your submission. In your Excel spreadsheet, clearly indicate the target cell, the cells corresponding to the decision variables and all the constraints. Also indicate whether you are minimizing or maximiz-

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Issues

Senate (Total = 100)

Senate Group 1 Senate Group 2 Senate Group 3 Senate Group 4

House of Representatives (Total = 435)

House Group 1 House Group 2 House Group 3 House Group 4

President (Total = 1)

President

Y Y Y Y N N D Y

Y Y Y Y N N D Y

N D

N N Y 32 D N D 16 Y Y Y 30 N D Y 22

N N Y 140 D N D 75 Y Y Y 155 N D Y 65

Y Y Y 1

Number of Votes

Table. Stance on Budget Issues: "Y" = yes, "N" = no, "D" = don't care

Figure 1: Stance on budget issues.

ing the target cell. Include a second spreadsheet in your Excel file which displays all the formulas used in your optimization model.

In addition submit a non-technical consulting report (roughly 1/2 a page) that highlights your findings. The report should be prepared as if to be presented to an audience that has little knowledge of quantitative models.

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Farm Aid

United Nations

Social Security