Modified Chaplygin Gas with Variable G and $\Lambda$

In this work, we have considered modified Chaplygin gas with variable G and $\Lambda$. The trivial solution describes decelerating phase to accelerating phase of the universe. The non-static with constant equation of state describes the inflationary solution. For static universe, G and $\Lambda$ must be forms arbitrary and for static universe with constant equation of state G and $\Lambda$ should be constant.