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)
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
- Is carbon dating? Why does it work? Give an example in which carbon dating would be useful.arrow_forwardRedo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?arrow_forwardEXERCISES Maximum Sustainable Harvest Find the maximum sustainable harvest in Exercises 7 and 8. See Example 6. f(S)=12S0.25arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage