Answer
See below.
Work Step by Step
We evaluate $z$ at the corner points:
$(0,6):z=5(0)+7(6)=42$
$(5,6):z=5(5)+7(6)=67$
$(5,2):z=5(5)+7(2)=39$
$(4,0):z=5(4)+7(0)=20$
$(0,3):z=5(0)+7(3)=21$
Thus the maximum value is $67$, the minimum value is $20$.
