Chapter 6.3, Problem 57E

In Problems 49-58, construct a mathematical model in the form of a linear programming problem. (the answers in the back of the book for these application problems indicate the model.) then solve the problem by applying the simplex method to the dual problem.

Education: resource allocation. A metropolitan school district has two overcrowded high schools and under-enrolled high schools. To balance the enrollment, the school board decided to bus students from the overcrowded schools to the inderenrolled schools. North Division High School has $300$ more students than normal, and South Division High School has $500$ more students than normal. Central High School can accommodate $500$ additional students. The weekly cost of busing a student from North Division to the Central is $\text{\$}5$, from North Division to Washington is $\text{\$}2$, from South Division to Central is , and from South Division to Washington is $\text{\$}4$. Determine the number of students that should be bused from each overcrowded school to each underenrolled school in order to balance the enrollment and minimize the cost of busing the students. What is the minimum cost?