I can't find in the documentation that the input expressions need to be exact numbers, but if you look at all the examples of FindInstance
, you see they all use rational numbers. So rationalize your expression and it works,
FindInstance[Rationalize[{a, b} > 0.27 && a == 10^8 && b == 2], {a, b}]
(* {{a -> 100000000, b -> 2}} *)
There is some bug going on here, you can see that for some values FindInstance
returns an answer, while for others it does not,
{wk, nwk} =
Reap[Do[If[
Length@FindInstance[a == 10^8 && b == 2 && {a, b} > n, {a, b}] <
1, Sow[n, tag1], Sow[n, tag2]], {n, 0, 1, .01}]][[2]]
(* {{0., 0.03, 0.05, 0.06, 0.08, 0.09, 0.11, 0.14, 0.16, 0.17,
0.19, 0.2, 0.22, 0.25, 0.28, 0.3, 0.31, 0.33, 0.34, 0.36, 0.39,
0.41, 0.42, 0.44, 0.45, 0.47, 0.5, 0.53, 0.55, 0.56, 0.58, 0.59,
0.61, 0.64, 0.66, 0.67, 0.69, 0.7, 0.72, 0.75, 0.78, 0.8, 0.81,
0.83, 0.84, 0.86, 0.89, 0.91, 0.92, 0.94, 0.95, 0.97, 1.}, {0.01,
0.02, 0.04, 0.07, 0.1, 0.12, 0.13, 0.15, 0.18, 0.21, 0.23, 0.24,
0.26, 0.27, 0.29, 0.32, 0.35, 0.37, 0.38, 0.4, 0.43, 0.46, 0.48,
0.49, 0.51, 0.52, 0.54, 0.57, 0.6, 0.62, 0.63, 0.65, 0.68, 0.71,
0.73, 0.74, 0.76, 0.77, 0.79, 0.82, 0.85, 0.87, 0.88, 0.9, 0.93,
0.96, 0.98, 0.99}} *)
There is an error message which isn't reported,
Trace[
FindInstance[{a, b} > 0.27 && a == 10^8 && b == 2, {a, b}],
Message[___]]
(* {{Message[FindInstance::lpsnf], Message[Message::msgl,$MessageList]}}} *)
As far as I can tell, this message simply means no solution can be found,

FindInstance[a > 0.27 && b > 0.27 && a == 10^8 && b == 2, {a, b}]
. Did you try running it? Also, what do you mean what is my problem? My problem is thatFindInstance
doesn't find the obvious solution, and I'm trying to figure out how to make it work. $\endgroup$ – user541686 Mar 22 '16 at 9:53FindInstance[a > 27/100 && b > 27/100 && a == 10^8 && b == 2, {a, b}]
. Then decide how to formulate the problem. $\endgroup$ – Artes Mar 22 '16 at 9:56{a, b} > .27
is not a valid inequality (It is never true). Somewhat puzzled whySolve
works though. $\endgroup$ – george2079 Mar 22 '16 at 16:05>
is listable $\endgroup$ – Jason B. Mar 22 '16 at 18:51