@WD0HHU i am attaching the plot which i got after making the changes.

But during optimization it is showing error.

Attaching sheet: q1.mw

@WD0HHU Can you share the plot?

@Carl Love ok Thankyou. But whenever you are free please help me if possible. Thanks

@Carl Love Thankyou for reply. Want condition such that the function(TPpm(S1,Sp)) is concave (1st*principal minor should be < 0 and determinant should be <0). Is it possible? I am getting determinant =0. 
attaching sheet : q4.mw

@mmcdara I am using hessian matrix for proof of concavity.
Now i want condititions where the hessian matrix determinant is positive. and first principal minor is -ve. 
Can you provide the code for it. The sheet is attached in earlier question q3.mw.

@mmcdara THankyou. Map(simpify ) code not working showing error. Attaching sheet below

q3.mw

@mmcdara Do any of the condition printed above give positive definite?

@mmcdara Thankyou for reply. But what is C ? and why we assume it <0.

I have made some changes in my objective function and i had used hessian matrix for proof of concavity. Now i want condititions where the hessian matrix determinant is positive.

I am attaching the sheet, where determinant is -------    a*b>c^2    or  j1>j2 given in below sheet.
Can anyone help me to get the condition where determinant of hessian is positive.
q2.mw

@mmcdara Thankyou for the answer. But is it possible to get g1 in simplified way (readable format) and in g2 is expressed in wrong way as you can see in the screenshot which i have attached below:

the other query is, can we find the condition from hessian matrix for local maximum or minimum? 

@Thomas Richard Thankyou.

@acer What i understant is T1(i) and T2(i) gives positive root of t1 and t2 in form of i. Can we incorporate T1(i) and T2(i) in optimization of function TBCIE. Is there any mistake i am doing ? How to plot the TBCIE BY considering all constraints which i have considered in maximization function.
I am attaching sheet.q6m.mw

@Thomas Richard Thanks for answer it worked. One more question is it possible to get P in readable format? I mean exactly know what all variables are there in p , what is the power of every variable etc.

The answer I am getting by optimizing function TBCIE and the answer from graph are different. I think that i am making some mistake in plotting graph. The decision variables are i and q. 

I am attaching the sheet .q4m.mw

@acer Thankyou for your reply sir. Further I have substituted t1 and t2 in a function TBCIE and optimizing it for getting the optimal value of decision variables i and q. The optimal value we get using Maximize and the optimal value from graph(using plot 3D) are  different. Is it the problem with plotting the graph, how to plot 3D graph for the function TBCIE?

I am attching the sheet. q4m.mw