The Arrow$-$Debreu model has two states and two risky assets. The initial price vector is

$.$

The payoff matrix is:

$($a$)$ Find a portfolio replicating an at$-$the$-$money call option on asset $1.$

$($b$)$ Find a portfolio replicating an at$-$the$-$money put option on asset $2.$

$($c$)$ The investor purchased $4$ call options and $3$ put options. What portfolio replicates this combination of options?

$($d$)$ The initial value of the portfolio from $($c$)$ is