Question

A toy manufacturer ships a toy in one of two different size boxes. The small box contains 6 of the toy and the large box contains 10 of the toy.
A client orders no fewer than 100 of the toy. Based on his storage and sales needs, the client requires that he receive no more than 8 of the large boxes and no fewer than 6 of the small boxes.

The cost to the client for a small box is $4 and the cost to the client for a large box is $6. The client does not wish to exceed $200 for his order of toys.

Let x represent the number of small boxes and y represent the number of large boxes.


What constraints are placed on the variables in this situation?

Answer 1

Answer:

Let x represent the number of small boxes.

Let y represent the number of large boxes.

The client receive no more than 8 of the large boxes and no fewer than 6 of the small boxes.

$x \geq 6$

$y \leq 8$

The cost of small box is $4 and the cost to the client for a large box is $6. The client does not wish to exceed $200.

$4x+ 6y \leq 200$

The small box contains 6 of the toy and the large box contains 10 of the toy. A client orders no fewer than 100 of the toy.

$6x+10y \geq 100$

Answer 2

The constraints placed on the variables y and x in this problem are y≤8 and x≥6.