@acer I've made revisions for clarity. Please check only the attached sheet and ignore the previous one.

N1.mw

Decision variables are : sigma, nu, Q3.
Parameters are : x=0.25, y=0.6, C=1.5, rho= 0.6, delta = 0.5, Vr = 0.00015, d = 2*10^9, k = 2*10^8 . [given in the above sheet].

What I have done:
I have defined the Total cost function of a firm that is TC(sigma,nu,Q3), which is objective function
I have defined the constraints for the firm
I have substituted value of Q1 and Q2 in terms of sigma and nu as shown in attached sheet for all constraints and objective function. 

Now i have substituted data to all constraintes and objective function TC(sigma, nu, Q3).
I solved for hessian matrix, and added a constraint for the TC(sigma, nu, Q3) function to be positive definite.

Now with all constraints and all parameters inputed i tried to minimize the objective function for optimal sigma,nu,Q3 but its showing an error as below:

Can you help in solving this problem? 

@acer The parameters like k, rho, delta, x are constant it is not changing it is given and constant. But the above optimization resulted in changes in parameters?

Above problem i have restructured by changing all equation and parameters. I tried to do optimization of 3 variables TRC function with 5 constraints but it is showing error. 

What is the issue? we cant optimize 3 variable problem?
Attaching sheet:  Updated_model.mw

Note: If 3 variable optimization is not possible you can give Q2 = x*d - delta*`(Q1a+Q1b)from above constraint (That is C1) and solve

@mmcdara Thankyou.

@mmcdara I have run the code but its showing error as below:



Sheet attached: Basic_model_new.mw

@mmcdara Dont know to execute the loop.

I have made it easy, just help me in executing the loop below. I have also given Q1,Q1a,Q1b Q2 relationship as you mentioned. 

q2.mw

@mmcdara Actually, what I meant is that in the equation below, 'u' is included in alpha, whereas for beta, you have used I2.

TRC_ok := eval(TRC, {alpha = (u -> 0.02*exp(0.4*u)), beta = (u -> 0.2e-1*(1-exp(.5*I2)))})

Actually i want the sequence of decision in the below manner:

1. Set I1 to 0.

2. Set I2 to values 0, 1, 2, 3, 4, 5, and 6.

3.Calculate Q1a and Q1b, and then determine Q1 while maintaining all constraints.

4.Based on Q1, determine Q2 while keeping all constraints.

5.Calculate the TRC value while adhering to all constraints.

6.Repeat step 1 by changing the value of I1 to 1 and continue this process until I1 reaches 5

@mmcdara Thanks for reply. what is u? its not e8 its 10^8. Can you also consider the range of I1 AND I2?

Question.mw

@Carl Love In earlier solution given the Q1 is a function of alpha and beta. There is a relationship between Q1 and alpha and beta. Sould we substitute that first? I just want to get for different values of I1 and I2 by considering constraints C1,C2 and C3 get different minimum TRC value. Find Q1, Q2 respectively?

Attaching sheet below :
Question.mw

Note : Consider relationship of Q1 and alpha and beta in the model.

In the sheet everything is mentioned.

@mmcdara Thankyou for reply. Can you find Q1 and Q2, and Q1a and Q2a for different value of I1 and I2 in the range given in above sheet using some loop maybe FOR Loop?

@mmcdara Thankyou for reply. I have updated an edited sheet below with file name questions to make it simple and clear:
Can you go throgh it:
Question.mw 

@acer For your understanding i am attaching a sheet below you can go through it. I have mentioned my decision variables Q1 and Q2, and for all other parameters I have given values and ranges:

I want to get optimum value of Q1 and Q2 at minimum value of TRC. 

For different value of I1 and I2 what is optimum Q1 and Q2 :-  Range of  I1 is from 0 to 5 and     range of  I2 is from 0 to 6 
Need to use FOR LOOP

Question.mw