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Find positive numbers x and y satisfying the equation xyequals15 such that the sum 3xplusy is as small as possible. Let S be the given sum. What is the objective function in terms of one​ number, x? Sequals nothing ​(Type an​ expression.) The interval of interest of the objective function is nothing. ​(Simplify your answer. Type your answer in interval​ notation.) The numbers are xequals nothing and yequals nothing. ​(Type exact​ answers, using radicals as​ needed.)

User Rrazd
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1 Answer

1 vote

Answer:


x = √(5)\\\\y = (15)/( √(5) )

Explanation:

According to the information of the problem


xy = 15

And


S = 3x+y

If you solve for
y on the first equation you get that


y = {\displaystyle (15)/(x)}

then you have that


S = {\displaystyle 3x + (15)/(x) }

If you find the derivative of the function you get that


S' = {\displaystyle 3 - (15)/(x^2)} = 0\\

The equation has two possible solutions but you are looking for POSITIVE numbers that make
S as small as possible.

Then


x = √(5)\\\\y = (15)/( √(5) )

User Christian Metzler
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