We have to find out the range of P. In the sense, we have to find the minimum value of P which would be sufficient to prevent the block from moving down. Then we have to find maximum value of P which will just disturb the equilibrium to move up the plane.

Applying static conditions of equilibrium,

$∴Σ F_y (↑ +ve)=0 \\ ∴R_N-1000 \sin60=0 \\ ∴R_N=1000 \sin60=866.025N \\ ∴Σ F_x (→ +ve)=0 \\ ∴P_{min}+ μR_N-1000 \cos60=0 \\ ∴P_{min}= 1000 \cos60-0.15(866.025) \\ =500-0.15(866.025) \\ ∴P_{min}=370.096N \\ \text { To find } P_{max}:- \\ F.B.D: - $

Applying static conditions of equilibrium,

$∴Σ F_y (↑ +ve)=0 \\ ∴R_N-1000 \sin60=0 \\ ∴R_N=1000 \sin60=866.025N \\ ∴Σ F_x (→ +ve)=0 \\ ∴P_{max}- μR_N-1000 \cos60=0 \\ ∴P_{max}= 1000 \cos60+0.15(866.025) \\ =500+0.15(866.025) \\ ∴P_{max}=629.904N$

Hence between the forces of magnitude $370.096 N$ and $629.904 N,$ block will be in equilibrium.