Pectin Extraction An increase in world production of processed fruit has led to an increase in fruit waste. One way of reducing this waste is to find useful waste byproducts. For example, waste from pineapples is reduced by extracting pectin from pineapple peels (pectin is commonly used as a thickening agent in jam and jellies, and it is also widely used in the pharmaceutical industry). Pectin extraction involves heating and drying the peels, then grinding the peels into a fine powder. The powder is next placed in a solution with a particular pH level H, for 1.5 ≤ H ≤ 2.5, and heated to a temperature T (in degrees Celsius), for 70 ≤ T ≤ 90. The percentage of the powder F(H, T) that becomes extracted pectin is
a. It can be shown that F attains its absolute maximum in the interior of the domain D = {(H, T): 1.5 ≤ H ≤ 2.5, 70 ≤ T ≤ 90}. Find the pH level Hand temperature T that together maximize the amount of pectin extracted from the powder.
b. What is the maximum percentage of pectin that can be extracted from the powder? Round your answer to the nearest whole number. (Source: Carpathian Journal of Food Science and Technology, Dec 2014)
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