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)
- Finding mass transit fares The Municipal Transit Authority serves 150,000 commuters daily when the fare is 1.80. Market research has determined that every penny decrease in the fare will result in 1000 new riders. What fare will maximize revenue?arrow_forwardPopulation Growth These exercises use the population growth model. 8. Bacteria Culture It is observed that a certain bacteria culturehas a relative growth rate or 12% hour. but in the presence of an antibiotic the relative growth rate is reduced to 5% per Hour.initialnumber of bacteria in the culture is 22. Population,n after 24 hours for following conditions. (a) No antibiotic is present, so the relative rate is 12%. (b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning