Question

Help please! 10 points!

Answer 1

Let the number of chairs Gavin build per week is x and number of tables he builds per week is y.

It takes 4 hours to work on a chair and 10 hours to work on a table. So time taken to work on x chairs and y tables will be:

$Time=4x+10y$

Gavin wants to work for no more than 40 hours. So we can write the inequality as:

$4x+10y \leq 40$

It takes $10 worth of supplies to build a chair and $15 worth of supplies to build a table. So cost or worth of supplies for x chairs and y tables will be:

$Cost=10x+15y$

Gavin wants to spend no more than $80 on material. So we can write the inequality as:

$10x+15y \leq 80$

Thus the system of inequalities is:

$4x+10y \leq 40$
$10x+15y \leq 80$

We can observe the possible combinations from the graph of these inequalities, which is shown below:
a) 0 chair and 3 tables
b) 5 chairs and 2 tables
c) 8 chairs and 2 tables