The cost of designating a school as a magnet school differs by region, and is as follows
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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.
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