The cost of designating a school as a magnet school differs by region, and is as follows (in $millions):

Region 1	Region 2	Region 3	Region 4	Region 5	Region 6
$10	$15	$18	$20	$22	$25

Each region in the city must either have a magnet school or should be adjacent to a region with a magnet school. For example, to serve residents in Region 1, a magnet school must be in one of the following four regions: 1, 2, 3, or 6.

a) Write down algebraically a math program that minimizes the cost of opening magnet schools while serving all regions. Make sure to clearly define all decision variables, constraints, and the objective function.

b) Formulate a constraint that does not allow the designation of both schools 2 and 3 as magnet schools.