The town of Blacksburg needs a larger modern middle school. The current middle school is in the center of town and is over 40 years old. There are two proposals for a new school—renovate and expand the current facility and keep it in town or build a new school on the outskirts of town. Different groups in town have strong feelings about the proposals. Some citizens want to retain the sense of tradition of the old school and like it in town, where it helps engender a sense of community. Others view the old school as antiquated and beyond saving and believe keeping the school in town near bars, traffic, and college students to be negative. The county school board will make the final decision.

The school board has asked several management science professors from the local college to use AHP to help evaluate the proposals. The school board has identified four groups from which it wants to solicit input regarding their preferences: the middle school PTA, the middle school teachers, current and former middle school students, and the town council. The management science professors have developed the following pairwise comparison matrices for each of these groups:

The school board's pairwise comparison of the four groups from which it is soliciting preferences is as follows:

a. Based on the AHP analysis conducted by the management science professors, which proposal should the school board select?

b. Check the school board's pairwise comparison of the criteria for consistency.

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PTA Proposal Renovate New Renovate 1/3 ew Teachers Proposal Renovate New Renovate 1/9 ew Students Proposal Renovate New Renovate New 1/2 Town Council Proposal Renovate New Renovate ew 1/5 Teachers Students Town Council 1/4 1/5 Group PTA PTA Teachers Students Town council 1/5 1/2 4 1/4 4