@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?

@Carl Love i have use double while loop but its showing error. buyback_policy_of_manufacturer.mw

@Carl Love w and q are related with a function given below. Can we add that inside the loop so that w cant take upper limit because q and w are inversely proportional (Condition given inside the maple file - highlighted in red Question.mw)

@Carl Love Q and q are same but given different notation for different cases.

I have another question similar to previous one here, I have 4 decision variable (p,Q,w and y). Where p and q are from the function E1., and w and y from the function E2. Please help me to solve the 2 equation simultaneously to get optimum decision variables. I am attaching the file below :-

Download buyback_policy_of_manufacturer.mw

@Carl Love I am extremely sorry. but that question consist of 4 variables which i parellelly working on. That question is all about when the manufacturer follows a buyback policy? I am extremely sorry i didnt know i can use the same id to ask 2 questions at a time. Please help me with this question. 

@Carl Love I have changed epsilon substitutution but i can't execute the algorithm properly inside the loop can you please help? I am again attaching the file by making changes.Please help.
maple_question.mw

@Carl Love thankyou so much.

@Carl Love table format for the above file attached below