Transporting troops' problem
A military detachment instructed by 40 engineers , 36 specialists dynamiters, 88 anti-guerrilla fighters, and 120 infants soldiers as support troop, must be transported to a important strategic position. At the base park there are 4 types of vehicles A, B, C, and D, conditioned for troops's transportation. People's number that each vehicle can transport is 10, 7, 6, and 9, in the way that details the following board:
| Engineers | Dynamiters | Anti-guerrilla fighters | Infants soldiers | |
| A | 3 | 2 | 1 | 4 |
| B | 1 | 1 | 2 | 3 |
| C | 2 | 1 | 2 | 1 |
| D | 3 | 2 | 3 | 1 |
The expenses of gasoline for each vehicle until the destination point is valued in 160, 80, 40, and 120 liters respectively. If we want to save gasoline, how many vehicles of each type will have to use to minimize the expenses of fuel?
Determining decision variables and expressing them algebraically. In this case:
- Xi: Number of vehicles of i type
- X1: Number of vehicles of A type
- X2: Number of vehicles of B type
- X3: Number of vehicles of C type
- X4: Number of vehicles of D type
Determining the restrictions and expressing them as equations or inequalities in function of the decision variables. Such restrictions can be obteined from soldiers that must be transported:
- Engineers: 3·X1 + X2 + 2·X3 + 3·X4 ≥ 40
- Dynamiters: 2·X1 + X2 + X3 + 2·X4 ≥ 36
- Anti-guerrillas: X1 + 2·X2 + 2·X3 + 3·X4 ≥ 88
- Infants: 4·X1 + 3·X2 + X3 + X4 ≥ 120
Expressing all implicit conditions established by the origin of variables: negativeness, integer, only a few allowed values... In this case, the restrictions are the quantities of vehicles that can't be negatives and also an integer number:
- Xi ≥ 0
- Xi are integers
Determining objective function:
- Minimize Z = 160·X1 + 80·X2 + 40·X3 + 120·X4