Barrick Gold mines and refines ore and sells pure gold in the global market. To raise

funds, it sells a derivative security whose payoff is indexed to gold price per ounce $($ST$)$

as follows.

Payoff Condition

$0$ if ST $<=45$

$30($ST $45)$ if $45<$ ST $<=50$

$150$ if ST $>50$

How would you replicate the payoffs of this security with a combination of puts and

borrowing$/$lending$?$