Two grains, barley and corn, are to be mixed for animal food. Barley contains 1 unit of fat per pound, and corn contains 2 units of fat per pound. The total number of units of fat in the mixture are not to exceed 12 units. No more than 6 pounds of barley and no more than 5 pounds of corn are to be used in the mixture. If barley and corn each contain 1 unit of protein per pound, how many pounds of each grain should be used to maximize the number of units of protein in the mixture?