Chapter 6.4, Problem 47E

In Problems 39-47, construct a mathematical model in the form of a linear programming problem. Do not solve.

Transportation. Three towns are forming a consolidated school district with two high schools. Each high school has a maximum capacity of $2,000$ students. Town $A$ has $500$ high school students, town $B$ has $1,200$, and town $C$ has $1,800$. The weekly costs of transporting a student from each town to each school are given in the table. In order to balance the enrollment, the school board decided that each high school must enroll at least $40\text{\%}$ of the total student population. Furthermore, no more than $60\text{\%}$ of the students in any town should be sent to the same high school. How many students from each town should be enrolled in each school in order to meet these requirements and minimize the cost of transporting the students?