Figure $1$

A particle of mass $2kg$ lies on a rough plane. The plane is inclined to the horizontal at $30.$ The coefficient of friction between the particle and the plane is $\frac{1}{4}.$ The particle is held in equilibrium by a force of magnitude $P$ newtons. The force makes an angle of $20$ with the horizontal and acts in a vertical plane containing a line of greatest slope of the plane, as shown in Figure $1.$ Find the least possible value of $P.$