A cooperative is looking at diversifying a fraction of its corn to ethanol. It receives 150 billion bushels annually. The cooperative is considering the option to convert a portion of its corn to ethanol with a constant conversion cost of 11 cents per bushel. The expected return for corn is 90 cents per bushel with a standard deviation of 5 cents. The expected return for ethanol is $1.10 per gallon with a standard deviation of 8 cents.

What is the theoretical optimal proportion of corn and ethanol for this coop? (for simplicity assume that no risk-free investment exists.)