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Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288?

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9 years ago
 Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288? This is calculus optimization problem. In a book answers are 12 and 24.Please show how you did it.Thank you. Read 2245 times 2 Replies
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smartgirl777smartgirl777
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9 years ago

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wrote...
9 years ago
 Let x and y be the two numbers so that S=2x+y and xy=288.Solve the second equation for one of the variablesx=288/y.Plug this in to the first equation.S=576/y+yTake the derivative.dS/dy=-576/y^2+1Set dS/dy = 0 and solve for y.y^2-576=0y=2424x=288x=12
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