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 the journey, we need to determine how many of each type of vehicle will be needed to transport the supplies and people.
Let's start by determining the maximum number of people that can be carried by the available vehicles:
- Each Landmaster can carry 6 people.
- Each Sandrover can carry 5 people.
Since we need to transport 80 people, we divide the total number of people by the maximum number of people each vehicle can carry:
Number of Landmasters needed = 80 / 6 = 13.33 (round up to 14)
Number of Sandrovers needed = 80 / 5 = 16
Therefore, we need at least 14 Landmasters and 16 Sandrovers to transport the 80 people.
Now let's determine the maximum amount of supplies (in kilograms) that can be carried by the available vehicles:
- Each Landmaster can carry 900kg of supplies.
- Each Sandrover can carry 1350kg of supplies.
Since we need to transport at least 18 tons (18,000kg) of supplies, we divide the total amount of supplies by the maximum amount of supplies each vehicle can carry:
Number of Landmasters needed = 18,000 / 900 = 20
Number of Sandrovers needed = 18,000 / 1350 = 13.33 (round up to 14)
Therefore, we need at least 20 Landmasters and 14 Sandrovers to transport 18 tons of supplies.
Now let's consider the availability of vehicles. We have 12 of each type, but we need more than 14 Landmasters and 20 Sandrovers.
To minimize the number of vehicles needed, we could use 12 Landmasters and 14 Sandrovers since they are the limiting factor in this case. This will accommodate 72 people and carry 15,300kg of supplies, which is below the required amounts.
Therefore, the smallest number of vehicles necessary for this journey is 12 Landmasters and 14 Sandrovers.
To find the smallest number of vehicles necessary for this journey, we need to determine the combination of Landmasters and Sandrovers that can carry at least 18 tonnes of supplies and 80 people.
Let's start by breaking down the requirements:
Supplies:
Each Landmaster can carry 900 kg of supplies.
Each Sandrover can carry 1350 kg of supplies.
People:
Each Landmaster can carry 6 people.
Each Sandrover can carry 5 people.
We have 12 Landmasters and 12 Sandrovers available.
Now, we will set up a system of equations to represent the constraints:
Let L = Number of Landmasters used
Let S = Number of Sandrovers used
Supplies equation: 900L + 1350S >= 18000 (18 tonnes = 18000 kg)
People equation: 6L + 5S >= 80
We want to find the minimum values of L and S, so we can solve this problem as an optimization problem.
Using trial and error, we can test different values of L and S to satisfy the equations:
L = 2, S = 4:
Supplies: 2 Landmasters * 900 kg + 4 Sandrovers * 1350 kg = 8100 kg + 5400 kg = 13500 kg (less than 18000 kg)
People: 2 Landmasters * 6 people + 4 Sandrovers * 5 people = 12 people + 20 people = 32 people (less than 80 people)
L = 3, S = 4:
Supplies: 3 Landmasters * 900 kg + 4 Sandrovers * 1350 kg = 13500 kg + 5400 kg = 18900 kg (more than 18000 kg)
People: 3 Landmasters * 6 people + 4 Sandrovers * 5 people = 18 people + 20 people = 38 people (more than 80 people)
L = 3, S = 3:
Supplies: 3 Landmasters * 900 kg + 3 Sandrovers * 1350 kg = 13500 kg + 4050 kg = 17550 kg (less than 18000 kg)
People: 3 Landmasters * 6 people + 3 Sandrovers * 5 people = 18 people + 15 people = 33 people (less than 80 people)
L = 3, S = 2:
Supplies: 3 Landmasters * 900 kg + 2 Sandrovers * 1350 kg = 13500 kg + 2700 kg = 16200 kg (less than 18000 kg)
People: 3 Landmasters * 6 people + 2 Sandrovers * 5 people = 18 people + 10 people = 28 people (less than 80 people)
L = 4, S = 2:
Supplies: 4 Landmasters * 900 kg + 2 Sandrovers * 1350 kg = 18000 kg (equal to 18000 kg)
People: 4 Landmasters * 6 people + 2 Sandrovers * 5 people = 24 people + 10 people = 34 people (less than 80 people)
Based on these calculations, the smallest number of vehicles necessary for this journey is 4 Landmasters and 2 Sandrovers.