Facing Local Minima Problem using SLSQP Optimizer
We don't have the whole model, so bring limited to work with partial information, here are some remarks:

The max Exp(sum()) objective can be replaced by max sum() (as exp() is monotonic). 
For global optimization problems, I often use solvers like Baron, Couenne, and Antigone. The problem may be small enough to prove global optimality.
You can also try a multi-start approach: use multiple different starting points. This will at least prevent some really bad solutions. Some solvers have this built-in (e.g. Knitro) but it is not very difficult to implement this with a simple loop.
SLSQP is a local solver. In theory, you could use basinhopping + SLSQP but I am not sure this works correctly with constraints.
I have objective function for Revenue which is in the form of e^(beta1*log(P1) + beta2*log(P2) +....beta250*log(P250)) where P1,P2... P250 are price of certain items and beta1,beta2,... beta250.are elasticity coefficients from model. I would like to maximize Revenue and currently using SLSQP provided constraints on prices, units and guest count. The problem I am facing is optimizer is getting stuck at local minima (It return same o/p when I relax bounds on price by 5% or 10% or even more). I tried using manually written gradient and using approx_fprime. In both the cases it is getting stuck at local. I could not go with global optimizers as they take lot of time and we are planning to deploy optimizer in real time so that store managers can use it. Can you suggest some algorithm which do not have local minima problem and should converge in less than 30 to 45 secs. 
Thanks