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}}