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These are replies submitted by Andiguys

@acer Thankyou. I had made changes as suggested..But in some cases it is not giving results and its taking so much time. I have marked that in yellow background.

Attaching sheet:

@Carl Love Thankyou for reply.

The minimum value x can take is just above zero or as it approach near to zero from positive side. 

@acer  I apologize for the earlier inconvenience. I need assistance in creating a table or understanding the syntax to do so. I am having difficulty generating a table for different parameter values provided in the DATA section. In the attached sheet, mu and gamma are constant parameters in the DATA. However, I want to understand how changes in mu and gamma affect the results. At the end of the sheet, I have included an example to illustrate what I need and how I want the table to be generated. Thankyou

@acer Thank you for the feedback given so far. Thank you for your patience. I will try to resolve it myself. If I have some syntax issues, I will ask. Thank you for your time and consideration.

@acer Hi ! Can you look into above problem and can you please suggest on the mistakes i have made? If possible can you help in viisualizing the problem using earlier done. I think i had made some mistakes in syntax?

@acer Thankyou for reply!

I am attaching a new sheet in which i encounter some errors.
1. In the below sheet you will see q is function of p , and eta is a function of q. When in some function if i substitute the eta and q, I am not getting that function in the form of only p.  Example C1b, C2b in sheet.
2. I am unable to find the hessian matrix its showing some error.
3. Showing error in optimization. The image i am attaching below:

4. Showing error in plot. 


@mmcdara Can you look into below attached sheet. It is not considering constraint 1. If constraint 1 is removed then the sigma value is shown as zero. What can be reason that sigma is zero?


@acer Yes for Q3 whatever constraints it is given it holds.

Q3 + delta*(Q1 + Q2) >= x*d , we have as constraint now no need to equate it as in sheet N5. Q3 be an independent variable. 
 So the formula (  Q3 = x*d - delta*(Q1 + Q2))  for Q3 no longer hold. 
C5 constraint is included so the hessian matrix is positive definite, but the matrix is semi definite anyway you can avoid that. 

1 problem is implementing conditional term in objective function: Within R3, there is a term that is included in the objective function only if mu ≠ 0; otherwise, it is excluded. How can this indicator function be implemented in Maple. Screenshot attached:

Generating table will help me to analyze how change in parameter value of x and y lead to change in Quantity Q1,Q2,Q3 and Total cost (TRC).

For better understanding should i post a new question with the problem explained in detail and how the algorithm should work?

@acer In the objective function, the terms R1, R2, and R3 are summed. Within R3, there is a term that is included in the objective function only if mu ≠ 0; otherwise, it is excluded. How can this indicator function be implemented in Maple, and how can the TRC function be optimized with respect to sigma, nu, and Q3? Refer to the attached sheet for more details.

@acer Thankyou.


I'm very sorry for the confusion; I'm developing a model and have been struggling to determine the necessary terms and constraints due to frequent changes in variables and functions. Thank you for providing the 3D plot; it has given me a better idea of the changes needed in the model.

I have one question: I made changes to the model you provided and performed optimization. I calculated the Hessian matrix, but it is not positive definite. Does this mean that the solution I obtained is not a global optimum? I am attaching the updated sheet below

@acer Thankyou for response. I am still getting error for direct search attaching screenshot. I think its some syntax error:

Regarding plot: I want 3D plot in which nu and sigma are in x and y axis and TRC(sigma,nu,Q3) in z axis if possible, else by assuming Q3 = x*d - delta(Q1+Q2), if the above plot is possible then it would be helpful.

One question?
Why you have take nu = sigma in optimization?, it is also giving same result in direct search method there also nu and sigma are equal.

Are you setting a boundary conditions where the TRC is convex?

If you need an assumption to restrict the region for optimization then you can take Q3 = x*d - delta*(Q1+Q2) in place of nu = sigma.

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

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:

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

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