PROBLEM : The Gotham City School system has three high schools that serve the needs of five neighborhood areas. The capacities of the various schools and the size (number of high school students) and ethnic mix of each neighborhood are as shown:

The distances (in miles) from each neighborhood to each school are as shown:

A federal judge has ruled that no high school in the city can have more than 50 percent nor less than 30 percent minority enrollment. Assume that students bused from each neighborhood have the same ethnic mix as the whole neighborhood. You wish to devise a busing plan that will minimize the total number of student miles bused while meeting the judge's integration requirements, and at the same time guarantee that no student is bused more than 2.5 miles. Formulate a linear programming model to solve this problem. (Do not solve the problem.)