SOLUTION: Solve the optimization problem. Minimize S = x + 17y with xy = 17 and both x and y

SOLUTION: Solve the optimization problem. Minimize S = x + 17y with xy = 17 and both x and y > 0.

Question 1118953: Solve the optimization problem.
Minimize S = x + 17y with xy = 17 and both x and y > 0.
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.

Then your function to minimize is


S =  = .


Take the derivative on x and equate it to zero:


1 - 289/x^2 = 0  ====>  x^2 = 289  ====>  x = +/-17.


Answer.  The local extremum values of x  are  17  and  -17.


         In the domain  x > 0  only the solution x= 17 works.






Plot of the function  S =

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