Pertanyaan

A company, that rents small moving trucks, wants to purchase 25 trucks with a combined of 2,800 cubic feet. Three different types of trucks are available: a 10-foot truck with a capacity of 350 cubic feet, a 14-foot truck with a capacity of 700 cubic feet, and a 24-foot truck with a capacity of 1 ,400 cubic feet. How should the company purchase each type of the trucks?

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

There are four solutions: no small trucks, 10 medium trucks, and 15 large trucks 2 small trucks, 7 medium trucks, and 16 large trucks 4 small trucks, 4 medium trucks, and 17 large trucks 6 small trucks, 1 medium truck, and 18 large trucks Suppose: Small truck is Medium truck is Larga truck is with . The mathematical model is shown below: Because the number of equations is less than the number of variables, you can not use a matrix equation to solve this problem. The solution is most easily found using an augmented matrix. Here is the augmented matrix: where: We are free to alter the value of as long as neither nor becomes negative (since you can not have a negative number of trucks). Suitable values for are 15, 16, 17, and 18: You can easily verify that, for each solution, the number of trucks is 25 and the fleet capacity is 28,000 cubic feet.

There are four solutions:

no small trucks, 10 medium trucks, and 15 large trucks
2 small trucks, 7 medium trucks, and 16 large trucks
4 small trucks, 4 medium trucks, and 17 large trucks
6 small trucks, 1 medium truck, and 18 large trucks

Suppose:

Small truck is

Medium truck is

Larga truck is

with x comma y comma z greater or equal than 0 .

The mathematical model is shown below:

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y plus z end cell equals 25 row cell 350 x plus 700 y plus 1.400 z end cell equals cell 2.800 end cell end table

Because the number of equations is less than the number of variables, you can not use a matrix equation to solve this problem. The solution is most easily found using an augmented matrix.

Here is the augmented matrix:

where:

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus z end cell equals cell negative 30 left right double arrow x equals negative 30 plus z end cell row cell y plus z end cell equals cell 55 left right double arrow y equals 55 minus z end cell end table

We are free to alter the value of as long as neither nor becomes negative (since you can not have a negative number of trucks). Suitable values for are 15, 16, 17, and 18:

You can easily verify that, for each solution, the number of trucks is 25 and the fleet capacity is 28,000 cubic feet.

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