Question

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

i really need help i have no idea what to do

Answer 1

you were given two equations:
\( S = x + 17y \ this\ is \ the\ one\ you\ need\ to \ minimize\)
and \(xy = 17\)

first you need to use \(xy = 17\) for your constraint. think of a variable that you want to replace in the equation that you need to minimize.. for example let's take y.
rearrange \(xy = 17\) in terms of y
it will be \(y =17/x\) -->constraint
then use this equation to replace y in the equation you want to minimize and then get the derivative of the new equation. set the new equation to zero and solve for x.

Answer 2

Thanks for the help