Use the$$ two$-$stage method to solve. A brewery produces regular beer and a$$ lower$-$carbohydrate "light" beer. Steady customers of the brewery buy $12$ units of regular beer and $10$ units of light beer. While setting up the brewery to produce the$$ beers, the management decides to produce extra$$ beer, beyond that needed to satisfy the steady customers. The cost per unit of regular beer is $$$$35,000$ and the cost per unit of light beer is $$$$41,000.$ The number of units of light beer should not exceed twice the number of units of regular beer. At least $32$ additional units of beer can be sold. How much of each type of beer should be made so as to minimize total production$$ costs?