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[?] Solve an optimization problem using Maximize assuming integers numbers?

Posted 5 years ago

Can someone help me? I have a production mix problem that needs to be solved through the maximize function, but considering it is production my variable responses (in the function called m, n, o, p and q) can only be integers numbers, which I don't know how to express in function. Below the function and its restrictions:

Maximize[3.24 m + 6.2 n + 4.35 o + 4.06 p + 
  8.73 q, {1.17 m + 2.08 n + 1.73 o + 2.04 p + 1.66 q <= 2700, 
  3.85 m + 0.9 n + 0.91 o + 0.7 p + 0.89 q <= 4050, 
  1.46 m + 7.18 n + 2.88 o + 5.92 p + 11.47 q <= 5400, 2.74 m <= 2700,
   9.75 n + 8.01 o + 6.28 p + 3.81 q <= 6750, 3.35 n + 2.64 o <= 4050,
   1.16 o + 3.65 p <= 1080, 0.98 n + 3.57 q <= 1080, 
  4.79 m + 5.5 n + 5.53 o + 5.13 p + 5.32 q <= 11448, 
  2.19 m + 5.65 n + 5.17 o + 3.1 p + 3.94 q <= 5400, 
  2.18 m + 2.16 n + 2.20 o + 3.15 p + 2.34 q <= 3780, 
  16 m + 33 n + 25 o + 35 p + 30 q <= 30000, 
  1.2 n + 0.8 o + 1.1 q <= 700, 0.95 m + 1.1 p <= 1200, 1.5 q <= 300, 
  m + n + o + p + q <= 1400, 0.5 o + 0.3 p <= 400, 
  0.05 m + 0.13 n + 0.08 o + 0.13 p + 0.13 q <= 180, n <= 450, 
  o <= 150, n + 7 q <= 1000, 600 <= m <= 920, 70 <= n <= 300, 
  15 <= o <= 90, 15 <= p <= 30, 20 <= q <= 100}, {m, n, o, p, q}]
POSTED BY: fernanda lima
Posted 5 years ago

Hi Fernada,

Restrict the domain to Integers.

Maximize[3.24 m + 6.2 n + 4.35 o + 4.06 p + 
  8.73 q, {1.17 m + 2.08 n + 1.73 o + 2.04 p + 1.66 q <= 2700, 
  3.85 m + 0.9 n + 0.91 o + 0.7 p + 0.89 q <= 4050, 
  1.46 m + 7.18 n + 2.88 o + 5.92 p + 11.47 q <= 5400, 2.74 m <= 2700,
   9.75 n + 8.01 o + 6.28 p + 3.81 q <= 6750, 3.35 n + 2.64 o <= 4050,
   1.16 o + 3.65 p <= 1080, 0.98 n + 3.57 q <= 1080, 
  4.79 m + 5.5 n + 5.53 o + 5.13 p + 5.32 q <= 11448, 
  2.19 m + 5.65 n + 5.17 o + 3.1 p + 3.94 q <= 5400, 
  2.18 m + 2.16 n + 2.20 o + 3.15 p + 2.34 q <= 3780, 
  16 m + 33 n + 25 o + 35 p + 30 q <= 30000, 
  1.2 n + 0.8 o + 1.1 q <= 700, 0.95 m + 1.1 p <= 1200, 1.5 q <= 300, 
  m + n + o + p + q <= 1400, 0.5 o + 0.3 p <= 400, 
  0.05 m + 0.13 n + 0.08 o + 0.13 p + 0.13 q <= 180, n <= 450, 
  o <= 150, n + 7 q <= 1000, 600 <= m <= 920, 70 <= n <= 300, 
  15 <= o <= 90, 15 <= p <= 30, 20 <= q <= 100}, {m, n, o, p, 
  q}, Integers]

(* {6085.2, {m -> 895, n -> 300, o -> 90, p -> 15, q -> 100}} *)
POSTED BY: Rohit Namjoshi
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