Question 3
Three food shops $A,B,C$ form a triangle $ABC$ with $\angle CAB=30^\circ$ and $AB=0.75AC$. They regularly supply noodles to the local population in the ratio $5:4:3$, respectively. Where should a noodle-weighing station $M$ be placed to minimize transport costs, assuming the cost is proportional to both the quantity and the distance transported?