Question

Two woodworkers, Tom and Carlos, bring in $100 for making a table and $80 for making a chair. On average, Tom must work 3 hours and Carlos 2 hours to make a chair. Tom must work 2 hours and Carlos 6 hours to make a table. If neither wishes to work more than 42 hours per week, how many tables and how many chairs should they make to maximize their income?

Answer 1

For x tables and y chairs, we want to

maximize p=100x+80y subject to
3x+2y <= 42
2x+6y <= 42

Now use your favorite linear programming tool to find that they make the most with

12 tables and 3 chairs.