my approach is as follows

1. freebody diagram with , frictional forces on wall and floor and normal forces + weight + couple M

2. resolve forces (2 equations)- M has no contributiion

3. taking moments from centre ( M present)

4 two inequalities for F< mu R for floor and wall

gives 5 equations ,

5. get all quantities using 3 equations taking one frictional force as parameters

6. plug in that in two inequalities which will give X>F>Y inequality

7. from that i got X>y which tells me what my M is

I dont seem to get the book answer which is Wg(mu)(mu+1)/(mu^2+1)

have i missed something?