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I am solving the following model in R and Lingo. However, I am getting an incorrect result. Do you know where my error is?

Model

minimize $10,773 * gt_1 + 30,094.7 * gt_2 + 684 * def$

subject to: $gt_1 + gt_2 + def + ghu = 1200$

$va + vt + vv = 8607.04$

$-0.2275 * vt + ghu = 0$

$7000 \leq va \leq 12540$

$0 \leq vt \leq 6412.97$

$0 \leq ghu \leq 1458.86$

$gt_1, gt_2 \in \{0,1\}$

Results from my implementation:

$gt_1 = 0$
$gt_2 = 0$
$def = 834.3984$
$ghu = 365.6016$
$va = 7000 $
$vt = 1607.040 $
$vv = 0$

Objective value = 57,0728.5

Given solution:

$gt_1 = 1 $
$gt_2 = 1 $
$def = 20.4 $
$ghu = 365.6 $
$va = 7000 $
$vt = 1607.04 $
$vv = 0$

Objective value = 54,820.21

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    $\begingroup$ What is the domain of the variables $def$ and $vv$? (E.g., can they take on any value; are they constrained to be non-negative?) $\endgroup$ – E. Tucker Apr 2 at 18:17
  • $\begingroup$ 0 <= vv < Inf and 0<= def. $\endgroup$ – Marco Oliveira Apr 3 at 1:22
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When I implemented the model (using AMPL/CPLEX), I got the same results as you did.

However, note that the given solution is not feasible for the given model. E.g., for the first constraint ($gt_1+gt_2+def+ghu = 1200$), the sum of the variables from the given solution is $388$, not $1200$ as required. This tells us that either the given model is wrong or the given solution is wrong.

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