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Optimized Move of a Crate

A force is applied to move a heavy crate across a horizontal surface. The coefficient of friction of the crate and surface is 0.3 (μ = 0.3). The crate is modeled as an extended body. The sketch shows its free-body-diagram and the orientation of the applied force. The event is that the crate is pushed a distance, L, to the right.

a) Obtain a general expression for the least magnitude of the applied force required, as a function of the angle of application of that force, θ.

b) Calculate the required force and work of the event for the angle of application, θ = 0

c) Calculate the least force required to accomplish the event and the least work.

Below is incomplete. When someone asks, I'll complete it.
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