tables can be made with 240 unused carpentry hours but only 50 tables can be made with 100 finishing hours.
Therefore we decide to make 50 tables.
If 50 tables are made, then the
unused carpentry hours are reduced by 200 hours (4 h/table multiplied by 50
tables); the value changes from 240 hours to 40 hours. Making 50 tables results
in the profit being increased by $3500; the value changes from $0 to $3500.
40 chairs are made, then the number of tables are reduced by 20 tables,
the value changes from 50 tables to 30 tables. The replacement of 20 tables by
40 chairs results in the profit being increased by $600; the value changes from
$3500 to $4100.
The optimal solution (maximum
profit to be made) is to company 30 tables and 40 chairs for a profit of $4100.