detailed working and explanation

3. (Sundamm, Chapter 3 Emercz'se 13) A monopolist faces a downward sloping inverse-demand curve p(m) that satises 39(0) 0 such that p(:v*) = 0. Show that the Weierstrass Theorem can be used to prove the existence of a solution to this problem. (ii) Now suppose instead there is m' > 0 such that C(at) 2 mp(m) for all a: 2 33'. Show, once again, that the Weierstrass Theorem can be used to prove the existence of a solution. (iii) What about the case where p(:r) = 19 for all :1: (the demand curve is innitely elastic) and C(JI) > 00 as :1: > oo