10 points! 10: gavin builds furniture for a living. he sells chairs for $45 and tables for $70 each. it takes gavin 4 hours and $10 worth of supplies to build each chair. a table requires 10 hours and $15 worth of supplies to make. gavin wants to work for no more than 40 hours per week and spend no more than $80 on materials. write a system of inequalities and state 3 possible combos.

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:



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



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:



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



Thus the system of inequalities is:




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