Answer
$$
M_P=(537.5 \cos \theta+75 \sin \theta) \mathrm{lb} \cdot \mathrm{ft}
$$
Work Step by Step
$$
\begin{aligned}
& M_P=150 \cos \theta(43)+150 \sin \theta(6) \\
& =(6450 \cos \theta+900 \sin \theta) \mathrm{lb} \cdot \text { in. } \\
& =(537.5 \cos \theta+75 \sin \theta) \mathrm{lb} \cdot \mathrm{ft} \\\\
& \frac{d M_P}{d \theta}=-537.5 \sin \theta+75 \cos \theta=0 \quad \tan \theta=\frac{75}{537.5} \quad \theta=7.943^{\circ} \\\\
& \text { At } \theta=7.943^{\circ}, M_P \text { is maximum. } \\
& \left(M_P\right)_{\max }=538 \cos 7.943^{\circ}+75 \sin 7.943^{\circ}=543 \mathrm{lb} \cdot \mathrm{ft} \\\\
& \text { Also }\left(M_P\right)_{\max }=150 \mathrm{lb}\left(\left(\frac{43}{12}\right)^2+\left(\frac{6}{12}\right)^2\right)^{\frac{1}{2}}=543 \mathrm{lb} \cdot \mathrm{ft} \\
&
\end{aligned}
$$
