$1.$ A refinery processes $200,000$ barrels of crude oil per day with an average API gravity of $25.$ If the refinery's distillation unit can separate $40\%$ of the crude oil into light naphtha $($API gravity $60),$ how many barrels of light naphtha are produced daily?

$2.$ In a catalytic cracking unit, $30,000$ barrels of heavy oil with an average molecular weight of $250$ are processed. If the cracking process achieves a conversion efficiency of $85\%,$ how many kilograms of lighter products are produced, assuming an average molecular weight of $100?$