Each case costs the grocer $$10$ and sells for $$12.$ Unsold cases are sold to a local farmer $($who mixes the milk with feed for livestock$)$ for $$2$ per case. If there is a shortage, the grocer considers the cost of customer ill will and lost profit to be $$4$ per case. The grocer must decide how many cases of milk to order each week.

$10.$ How many cases of milk to order each week if the grocer follows the expected monetary value criterion?