I am working on a script (attached sheet) where I use a FOR loop to iterate over different values of varepsilon. Within each iteration, I perform the following steps:

1. I optimize the function R_out and obtain a result, denoted as Pc

2. I then substitute Pc into another function, L_out and optimize it to find the values of p1,p2, and the corresponding function value.

I follow a similar procedure for a second case as well.

However, I'm encountering an issue: I'm unable to successfully substitute the result from R_out into L_out within the loop. This is causing an error in execution.

Finally, I intend to generate a plot with varepsilon  on the x-axis and certain result variables on the y-axis in a single plot (as indicated at the end of the sheet).

Sheet: Question_New.mw

Can someone help me:

1. Fix the substitution error in the loop, and

2. Provide the correct syntax for generating the desired plot?

I'm optimizing a function with constraints, meaning the decision variable has both a lower and an upper bound. When I use the  (MAX) syntax in Maple, it returns the lower bound as the optimal value (Pc) along with the corresponding function value. However, when I plot the graph, it shows that the function actually reaches its maximum at the upper bound. What could be causing this discrepancy

Sheet:Q_result_1.mw

Suppose we have two equations, and all parameters involved are assumed to be positive. Is there a systematic way or syntax to determine whether C1>C2​ or vice versa? Additionally, can we derive specific conditions under which C1>C2​ holds

Sheet: Q_greater.mw

I need to create a slider plot for A10, A11, and A12 by varying the parameters theta, Pu, and a.
I have a syntax ready — could you suggest modifications to make it work correctly and generate the plot?

Additionally, is it possible to compute the values of A13 and A14 by substituting the obtained A10, A11, and A12 values for each combination of theta, Pu, and a from the slider plot?

Sheet attached: Slider_Q.mw

I have two conditions, A and B, which must both be greater than or equal to zero. However, when I try to solve the problem, I encounter an error.

Could you please help me resolve this?

Note: All the parameters, whether specified or not, are positive and greater than zero.
File : Q3.mw