Answer:
a) 12
b) 129
Step-by-step explanation:
a)
[tex]w, x \in \mathbb{Z}_{\ge 0}[/tex]
[tex]w>50\\x<40[/tex]
For the smallest value of [tex]w-x[/tex], we gotta figure out the smallest value for w and the highest value for x.
[tex]w>50 \Rightarrow \text{ smallest value is } 51[/tex]
For [tex]x[/tex], once [tex]-(-x)=x[/tex], we conclude that [tex]x[/tex] cannot be negative and therefore, [tex]x=39[/tex].
[tex]51-39=12[/tex]
b)
[tex]y, z \in \mathbb{Z}_{\ge 0}[/tex]
[tex]y<70\\z\leq 60[/tex]
For the largest value of [tex]y+z[/tex], we gotta figure out the highest value for y and z.
[tex]y<70 \Rightarrow \text{ highest value is } 69[/tex]
[tex]z\leq 60 \Rightarrow \text{ highest value is } 60[/tex]
[tex]y+z=69+60=129[/tex]
