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Two numbers (represented by A and B) when multiplied together produce a maximum value. Two times the first number (A) plus one times the second number (B) must alejas equal 48.

User Starko
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1 Answer

4 votes

Maximize
U=ab subject to
2a+b=48


b = 48-2a


U = ab = a(48-2a)


U = -2(a^2 - 24 a) =-2(a^2 - 24 a + 144) + 2(144) = -2(a-12)^2+288

That's clearly maximum when the squared term is zero, so


a=12


b=48-2(12) = 24


U=12(24)=288

Answer: a=12, b=24, max 288

User Puneet Shekhawat
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