The horizontal force that must be applied to the handle in order to move the door to the right is 75 lb.
To determine the horizontal force that must be applied to the handle in order to move the door to the right, we need to consider the forces acting on the door. The weight of the door, F, is 300 lb. We also have the coefficients of static friction between the rail and the door at A and B, which are 0.15 and 0.25, respectively.
First, let's calculate the force of static friction at point A. This can be done by multiplying the coefficient of static friction by the weight of the door.

Next, let's calculate the force of static friction at point B.

To move the door to the right, we need to overcome the force of static friction at point B. Therefore, the horizontal force that must be applied to the handle is 75 lb.