(Solved): a) (7 points) Convert the following mathematical program into an equivalent linear program. Please ...

a) (7 points) Convert the following mathematical program into an equivalent linear program. Please show your work. $$\begin{array}{rr}\min & (\max \{x?y,z\})\\ \text{ s.t.: }& \\ (1):& x+y=16\\ (2):& x+y+z?22\\ (3):& ?x?y??19\\ \text{ (4): }& x,y?0.\end{array}?$$ 2 b) (8 points) Can the original problem be converted into an equivalent linear program if we add separately each of the following constraint: i. (4 points) $$\frac{x?z}{21?x?y?z}?10$$ ii. (4 points) $$\frac{y?z}{?21+y?x}?5$$ If so convert the new constraint, if not explain why not.