SOLUTION: Find three positive numbers a, b, and c such that 18 times "a" plus 13 times "b" plus 8 times "c" equals 135, and such that the product of a, b and c is a maximum.
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Question 463627: Find three positive numbers a, b, and c such that 18 times "a" plus 13 times "b" plus 8 times "c" equals 135, and such that the product of a, b and c is a maximum. Answer by richard1234(7193) (Show Source):
The AM-GM inequality states that equality occurs when all the "terms" (18a, 13b, 8c) are equal, i.e. 18a = 13b = 8c = 135/9 = 15. Hence, a = 5/6, b = 15/13, and c = 15/8.
