Answer
See below.
Work Step by Step
We evaluate $z$ at the corner points:
$(0,6):z=7(0)+5(6)=30$
$(5,6):z=7(5)+5(6)=65$
$(5,2):z=7(5)+5(2)=45$
$(4,0):z=7(4)+5(0)=28$
$(0,3):z=7(0)+5(3)=15$
Thus the maximum value is $65$, the minimum value is $15$.
