among all pairs of numbers with a sum of 224, find the pair whose product is maximum.

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The pairs of numbers with a sum of 224 are (1,223), (2,222), (3,221), etc. The product is maximum when x(224-x) is maximum. This happens when x=112, so the product is 112^2=12544. If the numbers have to be different then one is 111 and the other 113, with a product of 12543.

There is no need to introduce fractions because the maximum product is 12544 made up of 112*112 which are not fractions. If the numbers are to be different then one number would be 112-a and the other 112+a, where a is the fraction which can be as small as you like.

by Top Rated User (1.2m points)

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