Question $4-12$ points

Greeks!

$\backslash$table$[[$Type$,$Position,Delta,Gamma$],[$Put$,140,-0\mathrm{.}10,0\mathrm{.}20],[$Call$,200,0\mathrm{.}30,0\mathrm{.}04]]$

a$.$ What are the Delta and Gamma of this portfolio of options? $(2$ points$)$

b$.$ Option A has a Delta of $0\mathrm{.}4$ and a Gamma of $0\mathrm{.}2.$ What position in Option A will make the from $($a$)$ portfolio Delta neutral? $(4$ points$)$

c$.$ Option B has a Delta of $-0\mathrm{.}4$ and a Gamma of $0\mathrm{.}3.$ What position in Options A and $B$ will make the portfolio from $($a$)$ both Delta neutral and Gamma neutral? $(6$ points$)$