The daily diet for hamsters contains a minimum of 24 g of fat, 36 g of carbohydrates, and 4 g of protein. The hamsters should be fed no more than five ounces of food a day.

There are two types of food: Food X and Food Y. Food X costs $0.20 per ounce, and Food Y costs $0.30 per ounce. Food X contains 8 g of fat, 12 g of carbohydrates, and 2g of protein per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce.

How many ounces of each type of food to be combined to minimize the cost?