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How is it possible to determine the maximum and maximizer of the following function? where I(x>0) = 1 if x>0, otherwise 0

f(x)= x-(x-c)(x-y-z)Boole[x>c]/v

with the assumptions that 0<=x<=v, v>0,c>0,y>0,z>0. When I add the indicator function, I don't know why it cannot solve the problem.

Assumptions[v> 0, c > 0, y > 0, z > 0]
Maximize[{x - ((-c + x) (y + x - z)Boole[x>c] )/v,   x >= 0 && x <= v}, {x}]

As another question, I am wondering why in the answer of the following integration, the

Integrate[1/v, {x, 0, Max[y - c, 0]},  Assumptions -> y > 0 && c > 0 && v > 0]
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  • $\begingroup$ Maybe Integrate[1/v, {v, 1, Max[y - c, 0]}, Assumptions -> y > 0 && c > 0 && v > 0] $\endgroup$
    – cvgmt
    Feb 9 at 0:02
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Add condition into Maximize

Maximize[{x - ((-c + x) (y + x - z) Boole[x > c])/v, x >= 0, x <= v, 
  v > 0, c > 0, y > 0, z > 0}, {x}]
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