$8.$A financial institution has the following portfolio of over$-$the$-$counter options on dollars:

$\backslash$table$[[$Type$,$Position,Delta,Gamma,Vega$],[$Call$,200,0\mathrm{.}6,2\mathrm{.}1,1\mathrm{.}5],[$Put$,-100,-0\mathrm{.}8,0\mathrm{.}6,0\mathrm{.}6],[$Call$,-250,0\mathrm{.}7,1\mathrm{.}7,1\mathrm{.}5]]$

A traded option is available with delta $0\mathrm{.}5,$ gamma $1\mathrm{.}25$ and Vega $1\mathrm{.}5.$

What position in the traded option and in dollars would make the portfolio both Gamma and Delta neutral?

What position in the traded option and in dollars would make the portfolio both Vega and Delta neutral?