Increasing the extrude through the piece

I want to get a shape which is extruded slowly, not as whole part. I mean I have a sketch and I want to extrude its right side less and left side more. just like lofted bose but by using extrude tool on a 2d sketch. Is this possible ?

Tried to visualize it on the attached file, Extrusion magnitude will increase through the red lines and the far side of the piece will be more extruded as the near side is less extruded.

SolidworksParts And Features