A furniture manufacturer makes wooden tables and chairs. The production process involves two basic types of labor: carpentry and finishing. A table requires 2 h of carpentry and 1 h of finishing, and a chair requires 3 h or carpentry and 1/2 h of finishing. The profit is $35 per table and $20 per chair. The manufacturer's employees can supply a maximum of 108 h of carpentry work and 20 h of finishing work per day. How many tables and chairs should be made each day to maximize profit?

Question

A furniture manufacturer makes wooden tables and chairs.  The production process involves two basic types of labor: carpentry and finishing.  A table requires 2 h of carpentry and 1 h of finishing, and a chair requires 3 h or carpentry and 1/2 h of finishing.  The profit is $35 per table and $20 per chair.  The manufacturer's employees can supply a maximum of 108 h of carpentry work and 20 h of finishing work per day.  How many tables and chairs should be made each day to maximize profit?

oobleck · Answer

you want to maximize p = 35x+20y subject to 2x+3y <= 108 x + 1/2 y <= 20 So now graph the region and pick maximum p at the vertices.