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maplemaximize

maximize equation subject to constraints in maple

I want to maximize this equation:

(k[m]*a-(a*r*k[m]-a*k[m]-b*c-b*c[m])/(2*(-1+r)))*((1-r)*(a*r*k[m]-a*k[m]-b*c-b*c[m])/(2*b*(-1+r))-c-c[m])

subject to constraints:

a > 0, b > 0, c > 0, r > 0, k[m] > 1, k[m]*a > (a*k[m]*(-1+r)-b*(c+c[m]))/(2*(-1+r)), a >= b*c, r < 1, a/b < (c[m]+c[r])/(k[m]*(-1+r)-r+1), a/b < (c+c[m])/(k[m]*(-1+r)), (c+cm)*b+a*k[m]*(-1+r) < 0

is it possible? if it is not, I want to know that equation could be positive or not and in what range of variables it could be positive?

Solution

  • Using Maximize() you can do it, here you can find how to do this: https://www.maplesoft.com/support/help/Maple/view.aspx?path=Optimization%2FMinimize

    Using Matlab you can do it using fminsearch()