Maximimize not working properly?

Question

I try to evaluate the Integer Maximum of a given function under constraints.

b = 31/10;l = 91/10;m = 91/10;d = 1/10;p = 2;

  B[n_, b_, l_, m_, d_, p_] := (b l (-1 + n))/(2 (1 + n)) - d n - 
  l (l/(m n p))^(1/(-1 + p)) ((1/p) - 1) 

If I compare,

N[B[15, b, l, m, d, p]]
NMaxValue[{B[n, b, l, m, d, p], n >= 1&& n \[Element] Integers}, n]

I see that NMaxValue does not return the maximum. Using MaxValue does not return a result at all.

So what is the right comman line for the maximization here?

Answer 1

Solution to the current question

Plot function B and check the the return value range of function B, narrow the question and give MaxValue decent inputs, MaxValue will have a better chance to give what you want.

In:

b = 31/10; l = 91/10; m = 91/10; d = 1/10; p = 2;
B[n_, b_, l_, m_, d_, p_] := (b l (-1 + n))/(2 (1 + n)) - d n - 
  l (l/(m n p))^(1/(-1 + p)) ((1/p) - 1)
B[15, b, l, m, d, p] // N;
Plot[B[n, b, l, m, d, p], {n, 1, 10000}]
Plot[B[n, b, l, m, d, p], {n, 1, 1000}](* n between 1 and 150 *)
MaxValue[{B[n, b, l, m, d, p], 
  150 >= n >= 1 && n \[Element] Integers}, n]

Out:

Solution to the previous question

The question is updated. The code below has nothing to do with the latest question. I haven't deleted it because I thought the other people might has the similar issues.

In:

Clear[R, F, HR, n]
b = 48/10;
l = 19/10;
m = 99/10;
d = 5/10;
p = 12/10;

R[n_, b_, l_, m_, d_, p_] := 
  1/2 l (b - (4 b)/(1 + n) + 2 (l/(m n p))^(1/(-1 + p)));
F[l_, m_, n_, b_, d_, p_] := -d + (b l)/(n + n^2) - 
   m ((l/(m n p))^(p/(-1 + p)));
HR[n_, b_, l_, m_, d_, p_] := 
  l/(m p (p - 1)) (n m p/l)^((p - 2)/(p - 1));

Maximize[{ R[n, b, l, m, d, p], b > HR[n, b, l, m, d, p] , 
  F[l, m, n, b, d, p] > 0  , n >= 1 }, n \[Element] Integers]
Maximize[{R[n, b, l, m, d, p], b > HR[n, b, l, m, d, p], 
  F[l, m, n, b, d, p] > 0, n > 1}, n \[Element] Integers]

Out:

{29403675625/35939207332188864, {n -> 3}}
{29403675625/35939207332188864, {n -> 3}}