Consider a non$-$dividend paying stock whose price today is $$30$ and a year from now will be $$40$ or $$25.$ Assume that the risk$-$free rate with continuous compounding is $4$ percent per year. Under the one$-$period model, determine.

$($a$)$ The number of shares in the portfolio that replicate a one$-$year European call with a strike of $$30.$

$($b$)$ The amount of risk$-$free investment in the portfolio that replicates a one$-$year European put with a strike of $$35.$