PLEASE EXPLAIN YOUR SOLUTION A small company that manufactures two models of exe

Question

PLEASE EXPLAIN YOUR SOLUTION

A small company that manufactures two models of exercise machines has an order for 15 units of the standard model and 15 units of the deluxe model. The company has trucks of two different sizes that can haul the products, as shown in the table.

Find a system of inequalities describing the numbers of trucks of each size that are needed to deliver the order. (Use x for the number of large trucks and y for the number of medium trucks.)

Truck Standard Deluxe Large 6 3 Medium 4 6

Explanation / Answer

Let x be the number of large trucks and y be the number of medium trucks used by the company to haul the products. Then

6x+4y = 15…(1) and 3x+6y = 15…(2).

The augmented matrix of this linear system is A(say) =

6

4

15

3

6

15

The RREF of A is

1

0

5/4

0

1

15/8

On rounding off to the next higher whole number, we have x = 2 and y = 2. Hence,

minimum number of large trucks:           

2

minimum number of medium trucks:    

2

minimum units of standard model:         

15

minimum units of deluxe model:

15

6

4

15

3

6

15

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