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
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.