Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of lemon-lime soda to make 12 cups. He pays $3.00 for a 2-liter container of lemon-lime soda and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit
To make 12 cups of punch, Rafael needs 2 liters of lemon-lime soda, which is 2 liters * 4 cups/liter = <<2*4=8>>8 cups of soda.
He also needs a gallon of sorbet, which is 1 gallon * 16 cups/gallon = <<1*16=16>>16 cups of sorbet.
The total cost of the soda is $3.00 and the total cost of the sorbet is $4.00, so the total cost of the ingredients is $3 + $4 = $<<3+4=7.00>>7.00.
To make a $10 profit, Rafael needs to earn $7 (the cost of the ingredients) + $10 (the desired profit) = $7 + $10 = $<<7+10=17.00>>17.00.
Rafael will make 12 cups of punch, so he needs to charge $17 / 12 cups = $<<17/12=1.42>>1.42 per cup of punch to make a $10 profit. Answer: \boxed{1.42}.