Answer
See below.
Work Step by Step
We evaluate $z$ at the corner points:
$(0,6):z=10(0)+(6)=6$
$(5,6):z=10(5)+(6)=56$
$(5,2):z=10(5)+(2)=52$
$(4,0):z=10(4)+(0)=40$
$(0,3):z=10(0)+(3)=3$
Thus the maximum value is $56$, the minimum value is $3$.