$1.$ A refinery processes $200,000$ barrels of crude oil per day. If the yield of gasoline is $40\%,$ diesel is $30\%,$ and other products make up the rest, how many barrels of each product are produced daily?

$2.$ In a catalytic cracking unit, $2,500$ barrels of heavy oil are processed, resulting in $1,800$ barrels of gasoline, $600$ barrels of diesel, and $100$ barrels of other products. What is the conversion efficiency of heavy oil to gasoline?