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These are questions asked by Katatonia


I have seen some examples of linear programming or integer programming in Maple. But, I am wondering how to solve a mixed-integer program when just some of the decision variables are integer and the rest are continuous? I would be thankful if you can share an example. 


Suppose I have an expression denoted by Q3. I also have two other expressions such as Q1, Q2. I wanna write Q3 as a convex combination of Q1 and Q2, for example, Q3 = gamma*Q1 + (1-gamma)*Q2 where 0<gamma<1. How is it possible?

Q3 = 1/(v)*(    v*pi-  (   (1-alpha*gamma) *pi * r[0]  - (1-pi)*B*alpha  + (gamma*pi + (1-pi)*h)    )   )


Q2 = 1/v *(  v*pi    -  (   h - (1-pi)*B   )      )


Q1 = 1/v*(   v*pi     - (   pi*r[0]+ (1-pi)*h  )   )


I am not sure if is possible to write Q3 = gamma*Q1 + (1-gamma)*Q2 and it might be something like Q3 = gamma*Q1 + (1-gamma)*Q2 + constant



Suppose we have an unknown parametric function like g(x). We do not know the exact form but we know that g(x) is increasing and concave. Also, we define h(x) = g(x)*f(x) where we know the exact form of f(x) like f(x)=2x+5. Here, I want to investigate if the function h(x) is concave or not. How is it possible to do this?



I wanna shade/fill different areas in a single graph and provide a legend for the graph. Areas are defined as follows where 0<=x<=1 and 0<=z<=1. 

(label = c1) \quad if 0<x<1/13*(5-2sqrt(3)),0<z<1/2(2x+x^2)+1/2sqrt(4x^3+x^4)


(label = c2) \quad if 0<x<1/13*(5-2sqrt(3)),1/2(2x+x^2)+1/2sqrt(4x^3+x^4)<z<2x


I want to evaluate a parametric function to find intervals in which a condition is satisfied. For example, in the following instance, I know that 0<=c<=1 and 0<r<1. How can find intervals for r such that the following expression is less than 1?

-r+c+1 + sqrt(  r^2 - 2*r*c -r +2*c  ) <1,


0<=c<=1 and 0<r<1  and 

r in (0, min(1,2c) )

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