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Title: Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288? Post by: Smith11 on Apr 3, 2013 This is calculus optimization problem. In a book answers are 12 and 24.
Please show how you did it. Thank you. Title: Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288? Post by: smartgirl777 on Apr 3, 2013 Content hidden
Title: Find two positive numbers that minimize the sum of twice the first number plus second if product of two is 288? Post by: Juelz_9214 on Apr 3, 2013 Let x and y be the two numbers so that S=2x+y and xy=288.
Solve the second equation for one of the variables x=288/y. Plug this in to the first equation. S=576/y+y Take the derivative. dS/dy=-576/y^2+1 Set dS/dy = 0 and solve for y. y^2-576=0 y=24 24x=288 x=12 |