You manage a stock portfolio worth $$54$ million with a beta of $1\mathrm{.}7.$ You want to hedge the risk of a stock market downturn by using S&P $500$ index futures contracts with a contract multiplier of $250.$ The currentlevel of the S&P $500$ index is $2,990.$

A$)$ How many S&P $500$ index futures contracts do you need to trade to increase the beta of the portfolio from $1\mathrm{.}7$ to $2\mathrm{.}6($rounded to the nearest integer$)?$