Q:  If u(x,y)=x+y, Px=4, and Py=5,  What is the minimum income needed to achieve a utility of 10?

A:  Comparing MUx/Px which is 1/4 to MUy/Py which is 1/5, we know that this person always wishes to buy all x an no y.  Therefore for u(x,y)=10 it must be that x+y=10 and we already found that y=0.  Therefore, x=10.  As, Px=4, x=10, Py=5, and y=0 the minimum income is 4*10+5*0=$40.