I have downloaded DirectSearch package and its works fine. Thanks for this precious help.

As per the reply of  tomleslie 1597 ( application of DirectSearch command to my maple file maple_emailcopy2.mw), it is clear that my objective function (TP) is not concave for theta variable. This result is true for my specified values of the parameters in my problem. The parameter values specified is-

[alpha = 50, beta = .7, c = 20, h = 4, m = .4, o = 10, p1 = 40, s = 10, u = 5, a = 15000, b = 2]

My question is if I change any( or some or all) of the values of these parameter in my maple file, then there may be a possibility that my objective function (TP) would be concave with respect to five independent variables ( theta, T, E, W, tp). Thus, if any procedure is availble by which I systematecally change the values of these parameters to determine for which set of these parameters, my objective function would be concave with respect to above mentioned five independent variables. or I have to do it manually each time by trial and error method.

Thanks again for providing infor for DirectSearch method.

Regards,

Nilesh

Thank you very much Sir for your very good explanation. 

Sir, I have heard about a Maple addon package- "Optimisation toolbox". Should I insist my institute to purchase this addon so that I can try this problem or it may not be possible to solve this problem even with this addon.

Another thing is if I also want to use this addon "DirectSearch", how can I get this addon.

Thanks Sir for your reply.

Regards,

Nilesh

maple_emailcopy2.mw

Now I corrected the maple worsheet and again enclosed. Please find the link above. The remark for each equation is written for clarity. 

Thank you Sir for trying to help me. 

Thanks and Regards,

Nilesh

Please find the link of the total profit function. 

question_maple.mw

@tomleslie 

@tomleslie 

Thanks for early reply. Sorry for the incomplete statement of the problem. There are three other variables 'q', 't1' and 'Q". These variables depends on the five independent variables. When I substitute the values of these three variables in the total profit function, the total profit function equation is enclosed in the maple file question_maple.mw 

The following Total profit function equation is stated in terms of only five independent variables (E,W, T, theta, p1). 

Thank you Sir for your reply.

Download question_maple.mw
 

Download question_maple.mw