Thanks!!!!

Since you can easily solve your second equation for x, substitute that result for x into your first equation and give that

min 3(350-y^0.1)+0.7y for y

to WA and this almost instantly gives you the minimum and the y value.

WA

Then you can use that result to find the x value.

When Wolfram|Alpha does not seem to be able to solve a problem I have found a powerful trick is to try to divide the problem into two parts, let it solve the first part and use the result of that to solve the second part, giving the complete solution.

No, i am the beginner.

I got the result from local Wolfram L installation. You are right, Wolfram A has problems with it. I have no experience with A's performance re optimization problems.

I use exact numbers in 2D for the input and then numerize the semi-symbolic result, like this: $N\left[\text{Minimize}\left[\left\{3 x+\frac{7}{10}y,x+\sqrt[10]{y}=350\right\},\{x,y\}\right]\right]$

In 1D input format it would look like that (and then i press the <Enter>-key of the number block on my keyboard):

Minimize[{3 x + 7/10 y, x + y^(1/10) == 350}, {x, y}] // N

{1047.54, {x -> 349.09, y -> 0.390065}}