While exploring for oil, it was necessary to carry at least 18tones of supplies and 80 people into a desert region.

Two types of vehicles are available :landmaster and sandrovers. Each landmaster could carry 900kg of supplies and 6 people. Each sandrover could carry 1350kg of supplies and 5 people. If there were only 12 of each type in good running order, find the smallest number of vehicles necessary for this journey.

To find the smallest number of vehicles necessary for this journey, we can start by setting up equations based on the given information.

Let's assume we need L landmasters and S sandrovers.

The first equation is based on the weight carrying capacity of the vehicles:

Weight carried by landmasters: L * 900 kg
Weight carried by sandrovers: S * 1350 kg

Since we need to carry at least 18 tons of supplies, which is equal to 18,000 kg, the first equation becomes:

L * 900 + S * 1350 >= 18,000

The second equation is based on the number of people that can be carried:

People carried by landmasters: L * 6
People carried by sandrovers: S * 5

Since we need to carry at least 80 people, the second equation becomes:

L * 6 + S * 5 >= 80

Now, we need to check the minimum number of vehicles necessary, so we minimize both L and S. We can use a trial and error method to solve this.

Starting with L = 0 and S = 0:
0 * 900 + 0 * 1350 = 0
0 * 6 + 0 * 5 = 0

Since both equations are not satisfied, let's increase one of the variables by 1 and keep the other variable at 0.

Trying L = 1 and S = 0:
1 * 900 + 0 * 1350 = 900
1 * 6 + 0 * 5 = 6

Now, the weight requirement is not met (900 < 18,000). So, let's try the next combination.

Trying L = 0 and S = 1:
0 * 900 + 1 * 1350 = 1350
0 * 6 + 1 * 5 = 5

Again, the weight requirement is not met. Let's increase the first variable again.

Trying L = 2 and S = 0:
2 * 900 + 0 * 1350 = 1800
2 * 6 + 0 * 5 = 12

Now, the weight requirement is still not met. Let's continue this process until we find a combination that satisfies both requirements.

Continuing this process, we find:

L = 4, S = 0:
4 * 900 + 0 * 1350 = 3600
4 * 6 + 0 * 5 = 24

L = 3, S = 1:
3 * 900 + 1 * 1350 = 4950
3 * 6 + 1 * 5 = 23

L = 2, S = 2:
2 * 900 + 2 * 1350 = 5400
2 * 6 + 2 * 5 = 22

L = 1, S = 4:
1 * 900 + 4 * 1350 = 6300
1 * 6 + 4 * 5 = 26

L = 0, S = 6:
0 * 900 + 6 * 1350 = 8100
0 * 6 + 6 * 5 = 30

Finally, we have found a combination that satisfies both requirements:

L = 2 and S = 2, which means we need two landmasters and two sandrovers to carry the supplies and people into the desert region.

Therefore, the smallest number of vehicles necessary for this journey is four.