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Introduction to Learn Online Maximize Study of rates of change is called calculus. Optimization is one of the techniques in calculus. It is used to determining the maximum or minimum value of real function. Optimization is also called as mathematical programming. Minimize is the study of finding minimum value of the real function. Maximize is the study of finding the maximum value of the real functions. Both minimize and maximize referred to as optimization. In this article let us learn about maximize optimization online. Learn Online Maximize - Examples Let us learn some maximize problems online. Example 1: There are 60 mango trees. Each tree produces 900 mangos. For each additional tree planted. The output per tree drops by 30 mangos. How many trees should be added to maximize the total output of trees? Solution: Let x be the additional trees planted. P = (number of mango trees) ( mango output per tree) = (60 + x) (900 - 30x) = 54000 - 1800x + 900x - 30x2. = 54000 - 900x - 30x2 Now differentiate this equation, getting P’ = 900 - 60x = 20 (45 - 3x) =0 For x = 15 If x = 0 then P = 54000 If x = 15 then P = 54000 - 900 (15) - 30 (15^2) = 54000 - 13500 - 6750 Therefore, 33750 is the largest possible production of mangos. Example 2: There are 70 men in a company. Each man made 1000 chairs. For each make additional chairs. The output per man drops by 50 chairs. How many chairs should be added to maximize the total output of chairs? Solution: Let x be the additional chairs made. P = (number of man) ( chair made per man) = (70 + x) (1000 - 50x) = 70000 - 3500x + 1000x - 50x^2. = 70000 - 2500x - 50x^2 Now differentiate this equation, getting P’ = 2500 - 100x = 25 (100 - 4x) =0 x = 25 If x = 0 then P = 70000 If x = 25 then P = 70000 - 1000 (25) - 50 (25^2) =70000 - 25000 - 31250 Therefore, 13750 is the largest possible production of chairs. Learn Online Maximize - Practice Problem: A man working 80 hours per weak. Each weak he produces 1200 pots. For each additional pot produced. The output per week drops by 60 pots. How many pots should be added to maximize the total output of weak? Answer: 31200. Understand more on about cbse sample papers class 10 sa2 and its Illustrations. Between, if you have issue on these subjects maths models for class 10 cbse, Please discuss your feedback.
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