Greg works at Home Depot. He plans to mix gallon cans of purple passion and gallon cans of magenta madness. Greg has exactly 32 units of blue dye and 54 units of red dye. Each gallon of purple passion requires 4 units of blue dye and 1 unit of red dye. Each gallon of magenta madness requires 1 unit of blue dye and 6 units of red dye. Purple passion sells for $15 a can and magenta madness sells for $10 a can. How many gallons of each type of paint should Greg mix to maximize his profit?