Non linear programming optimization (which package to use?)

Hello,

1) Is there any nonlinear programming optmizer that I can user for the
following problem?

Obj function: (max) revenue = price * volume
Constraints: price and volume pair must be from the following variable data set:

Variable data set:
# price volume
1 10 500
2 20 450
3 30 330
4 40 250
5 50 190

Expected result: 10,000 (variable row#4)

2) Could it also be possible for the suggested non-linear programming
optimizer to accept formula (done with regression) and use it for
optimization purpose? If so, how?
Example:
Fitted to: revenue = -700price^2 + 5200price + 780
Subject to: price range between 10 to 50

Thanks,
Jerome