How can I organize the KKT conditions I derived into a table format?

Can you confirm whether the substitutions I made for the lower and upper bounds are correct?

KKT_Table_Q-22.mw

When optimizing with constraints, I’m getting an error: ‘NLP no feasible point’.

However, when I plot the graph, it shows a result — there appears to be a point where p1 is positive and s is maximized.

Could you help identify if there’s a syntax issue? Also, what’s the correct syntax to visualize the constraints in the plot?

Sheet: 07.mw

I need to export an image in high resolution in JPEG, JPG, and PDF formats. Right now, I'm using screenshots, which results in low clarity. Could you please help me with the correct syntax to generate a high-resolution, downloadable image in these formats? I'm attaching the file below:

q_new.mw

The two profit functions intersect at a certain point, but the graph is not clearly visible in the range of Cb​ from 30,000 to around 60,000. How can I adjust the plot to make this range more visible? What can i do such that two lines are seen distinct in that area?

Sheet:Q_12.mw

I'm working on an optimization problem involving a single decision variable p1, subject to four inequality constraints:

• Two upper bound constraints:

  p1 < b1,p1 < b2

• Two lower bound constraints:

  c1 ≤ p1,c2 ≤ p1

Effectively, the feasible region for p1 is:

max⁡(c1,c2)  ≤  p1  ≤  min⁡(b1,b2)

I have already formulated the Karush-Kuhn-Tucker (KKT) conditions for this setup, and now I'm trying to determine:

1. The optimal value p1∗​

2. The corresponding feasibility conditions

3. A case-wise breakdown depending on which constraints are active or inactive

Sheet:  Q_P1_Optimum_condition.mw