A year from now, one of two things will happen:

$($With $30\%$ probability$)$ Asset Y will cost $$17$ and Asset Z will cost $$68$ or

Asset Y will cost $$27$ and Asset Z will cost $$108.$

Assume that today, Asset Y costs $$20\mathrm{.}16$ and Asset Z costs $$80\mathrm{.}92.$ If there are no transaction costs and you can go long or short either asset, then what is your minimum arbitrage profit from trading assets Y and Z$?$ Assume that you can trade multiple units but not fractions of either asset.