Question $2.$

The block layout shown below consists of seven departments, all of equal size. The table at the right

indicates the relationships between the seven departments $($O: Okay, U: Unimportant, I: Important, E:

Especially important, A: Absolutely important$).$

$($a$)$ Determine the layout efficiency rating $($LER$)$ for the current layout.

$($b$)$ It is desired to improve the efficiency rating by rearranging departments. Determine a revised

layout that obtains $100\%$ LER, given that the building shape must remain the same, but the

departments can be moved around within the building.