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Question

Find the greatest value of x2y3 subject to the conditions 3x+4y=5, where x and y are positive numbers.

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Solution

x+x+y+y+y5[x2y3]1/53x+4y=5x+2x+y+y+2y5[2x22y3]1/5.5522/5[x2y3]1/5122/5[x2y3]1/5122x2y314x2y3

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