I need to only formulate a linear programming model for the problem on paper, not with the use of excel. Need statements (with variables) to represent the decision variables and a model to demonstrate the constraints. Do not need to solve the problem, just the model representing it.

The Gotham City School system has three high schools that serve the needs of five neighborhood areas. The capacities of the various schools are: The distances (in miles) from each neighborhood to each school are as shown: Neighborhood 3 4 School 1 2 Capacity (maximum enrollment) School A B 1.2 0.8 1.3 0.4 2.0 2.2 2.6 0.5 1.6 1.4 0.7 2.0 2.4 3.0 0.2 4.000 3,000 B Total 2.000 9,000 The size (number of high school students) and ethnic mix of each neighborhoods 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. Number of Students Percent Minority Students Neighborhood 2 3 4 5 Total 2,100 2,400 1,300 800 1.600 8,200 30 80 20 10 20 Formulate a linear programming model to solve this problem. Use software to solve