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

I want both Pc and r(Pc) to be greater than or equal to zero. The only constraint is that all parameters for which I’ve provided data must remain positive. Can we identify the key parameters that significantly affect Pc? Also, what condition ensures that Pc ≥ 0? Ideally, I’d like Pc to be less than or equal to Pu. Could you suggest what changes in the numerical values I should make to ensure Pc becomes a positive value?

Attaching file: Q2.mw

Can we include a graph that shows how Pc changes with respect to variations in the most sensitive parameters?

I’m trying to simplify the results I obtained from two scenarios. In the first scenario, I have results labeled g1,g2,g3​, and in the second scenario, I have g_1, g_2, g_3​. The issue is that the expressions are quite lengthy, and I want to shorten them by identifying and substituting common sub-expressions.

Is there a method or syntax that can help me automatically detect repeated terms and substitute them with a variable to improve readability?

For example:

Let’s say:

x=2f+3d+4(d+h+k)j+f

y=1(d+h+k)+hf+4d

Here, the expression d+h+k appears in both x and y, so I can define a new variable:

A=d+h+k

and substitute it into the equations to make them more concise and readable.

Attaching the sheet: Difference_two_model.mw

I have two equations on either side of an inequality that contain like terms such as Am and Ce. Could you simplify the expressions by mathematically eliminating these common terms from both sides? For example, if we have an equation like x+y⋅d+hx=g⋅f+hx , it simplifies to x+y⋅d=g⋅f.

Additionally, please solve for Cv and Ce.

Note: All terms are positive except R0er and R0m​.

I am attaching the relevant sheet for reference. Q_12.mw

Could we create a plot with tau0 varying from 0.1 to 0.6 on the x-axis and profit on the y-axis displaying Rprof, Mprof, Tprof, T_Cprof all on the same graph?

Sheet attached : trial_question.mw