Question

Q2 The transport company uses three types of trucks (T1, T2 & T3) to transport 3 types of vehicles (VI. V2 & V3). The capacity of each truck in terms of 3 types of vehicles is given below:

VI

2

6

6

V2

3

V3

6

6

8

TI

12

T3

12

Using matrix method, Find:

a) The number of trucks of each type required to transport 58, 75 and 62 vehicles of V1, V2 and V3 types of vehicles.

b) The number of vehicles of each type which can be transported if the company has 15, 10 & 20 Trucks of each type respectively.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The answer will be x1=15, x2=x3= 10.

Given,

There are three types of trucks (T1, T2, and T3).

And three types of vehicles (V1, V2, and V3).

V1 V2 V3

2     3    6

6     3    6

6     3    8

To find:

1. The number of trucks required.

2. The number of vehicles of each type that can be transported if the company has a given number of trucks.

Solution:

Assume x1, x2, and x3 to be the number of trucks of type T1, T2, and T3.

According to the question,

2x1+3x2+6x3= 58.

6x1+3x2+6x3= 75.

6x1+3x2+8x3= 62.

|A| = 4 + 8 + 27 – 12 – 6 – 12 = 9

Therefore A inverse = $\frac{1}{9}$$\left[\begin{array}{ccc}1&2&3\\3&2&2\\2&3&2\end{array}\right]$.  

By solving it we get, x1=15, x2=x3= 10.