# What is the answer linear programming?

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

• 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?) – E. Tucker Apr 2 at 18:17
• 0 <= vv < Inf and 0<= def. – Marco Oliveira Apr 3 at 1:22

## 1 Answer

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.