There are currently two high schools in Squareville. They are called Squareville NorthEast and Squareville SouthWest. Assume that every student is classified as an artist or a businessman. Also assume that each student lives within one of 2 High Rise Villas. The number of students of each type as well as the distance in miles from each villa to each high school is given in the table below.

Villa Businessman Artist
Villa 1 34 46
Villa 2 67 23

Villa NorthEast SouthWest
Villa 1 1 0
Villa 2 0 1

It cost $6 to transport 1 student 1 mile.

Part A. What is the optimal solution if the superintendent is permitted to send all students to their closest school? (Please do not formulate this part as an LP).

Part B. A new state law says that each high school within a village must have an approximately equal percent of its total student body be artists and businessmen. In particular, it must have at least 45% artists and at most 55% artists. The goal of the village superintendent is to assign each student to one of the two high schools while minimizing the total transportation cost. Formulate a linear program to solve the superintendent's dilemma.

Hint: You can use the following 8 decision variables in your LP.

A1E: Number of Artists going from Villa 1 to NorthEast

A2E: Number of Artists going from Villa 2 to NorthEast

A1W: Number of Artists going from Villa 1 to NorthWest

A2W: Number of Artists going from Villa 2 to NorthWest

B1E: Number of Businessmen going from Villa 1 to NorthEast

B2E: Number of Businessmen going from Villa 2 to NorthEast

B1W: Number of Businessmen going from Villa 1 to NorthWest

B2W: Number of Businessmen going from Villa 2 to NorthWest