@tomleslie sorry my mistake but is it possible to find range of i where g2 is not complex?

Is it possible to find the range of decision variables (i and q) where function(g2) is not complex?
I am attaching the file.
q1M.mw

Also is there any code/format in maple such that function g2 is clear and readable.

@mmcdara Thanks for answer. If we again want to integerate the sol (with limit ti.....si) is it possible using maple. I am attaching the image of integeration and its answer.

@acer I am finding difficulty in optimizing the objective function with an additional term. I am attaching both files the earlier solved one and the later which shows error while solving. Please help.

Decision variable for both file are i and q.

Solved file : 1_case.mw

Unsolved file (Finding error while solving): det3.mw                          (All questions are marked in yellow box)

Pls help to resolve it. Thankyou.

@acer Is it able to possible to change g1 and g2 in readable format, Currently i cant read exactly which variable is multiplied with which one or divided with which one.
I am attaching the file below
M1D.mw

@Carl Love Thanks for reply. 

I have substituted g1 and g2 and i have done all calculations. Now i am stuck with Solving the equation with Maximizing objective function (TBCI), for the decision variable i and q. I have marked yellow in the sheet where i encounter error. Can you please check whether i have made correct substitution and tell me where i went wrong. Thankyou

Attaching sheet  det1.mw

@acer Ok. Thankyou

@acerThankyou for reply.  From graph that you generated we can see that maximum occurs at value of i less than 0.799. But the Maximize function gives the value of i as 0.7999. How can that be possible?

@tomleslie range of i is from 0 to 0.8 , which taken care by constraint eq3 and eq3a. If value of i is between 0 and 0.8 then complex number is not generated. But i think maple is not reading that constraint. How can i solve it? Is it possible to give range and constraint at the same time in NLPsolve?

@tomleslie Thankyou for your reply. Actually i had mad all changes you suggested still i am not getting solution. Pls find my modified worsheet. And pls help if possible. Thankyou.

Find_optimum_i_and_q.mw

I have changed Each constraint by spliting into two simple inequalities. And changed the objective function mistake of sqrt(-i). But still i am not getting the optimum value of i and q which maximize TBCI. It is showing error "Error, (in Optimization:-NLPSolve) could not store HFloat(3233180.1691675433)-HFloat(HFloat(infinity))*I in a floating-point rtable".

Can anyone help me to solve it?

I am attaching the modified worksheet hereFind_optimum_i_and_q.mw

@Carl Love F(z) is cumulative distribution function. Where z = Q-G,
g := (p) -> a - b*p:
G := g(p)

cdf of uniform distribution with range [-3500,1500].

@Carl Love Can we get new w value from that equation by substituting q optimum to the above equation?

@Carl Love Question is highlighted in red in file.buyback_policy_of_manufacturer.mw

Example graph

@Carl Love Yes they are equation can we add that inside the loop? to get optimum? if not how to ensure that the above relationship is satisfied?