An English wine merchant introduces two types of wine, A and B, from vineyards that are far away and after the process, puts it in bottles and thus produces his two own brands, the Fein Wein and Party Plonk. Both wines A and B cost 0.80 and 0.20 pounds per liter, respectively, including the processing and bottling. The Fein Wein consists of 60% wine A and 40% wine B while the Party Plonk has 20% wine A and 80% wine B. The merchant shop sells 2 pounds per liter from Fein Wein and 1.20 pounds per liter from Party Plonk. The processing, bottles and distribution cost 0.5 pounds per liter for both brands.
The merchant has agreed to buy at least 24,000 liters of wine A this year and there are available 120,000 liters most of wine B. It is estimated that sales of Fein Wein during the year will reach 50,000 liters but the demand for the Party Plonk is uncertain. The merchant has this year only 60,000 pounds to buy the wines A and B. How many liters of the two brands must the merchant produce to maximize his profit?