Write and solve a system of inequalities to model the following situation: A carpenter makes wooden chairs.
He has enough wood to make 30 chairs
He makes $60 profit on a dining chair and $90 profit on a rocking chair
It takes him 1 hour to make a dining chair and 2 hours to make a rocking chair
He only has 40 hours available to work on chairs
The carpenter wants to maximize his profit given the information above.
How many dining chairs and rocking chairs should he make?
How much profit does he earn?