Frontline Agricultural Processing Systems uses several ingredients to make wheat crackers. After several years of operations and testing, their scientists found high protein and carbohydrates in two of their ingredients, barley and corn. While an ounce of barley costs $$0\mathrm{.}25,$ an ounce of corn costs $$0\mathrm{.}46.$ While an ounce of barley provides $9$ mg of protein and $1$ mg of carbohydrates, an ounce of corn provides $7$ mg of protein and $5$ mg of carbohydrates. Recently, demand for wheat crackers has increased. To lower the overall cost of producing wheat Erackers, Frontline Agricultural Processing Systems will want to know how many ounces of barley and corn to include in each box of wheat crackers to meet the minimum requirements of $160$ milligrams of protein and $40$ milligrams of carbohydrates.

If the protein requirement is reduced by $12$ milligrams, what would be the new optimal cost? Round to $2$ decimal places.