Katatonia

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These are questions asked by Katatonia

Hello

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. 

Thanks

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

 

Thanks

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?

 

Thanks

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,

 given 

0<=c<=1 and 0<r<1  and 

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

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