3. A furniture company specializes in hand-painted furniture. They are considering adding two new furniture designs: a small storage cabinet and an end table. Each cabinet takes the carpenters a total of 8 hours to build and it takes the painters 4 hours to paint it. Each end table takes 6 hours of carpentry to build and 3.75 hours to paint. This next month, the carpenters have a total of 144 available hours between them to build the new furniture designs and the painters have 80 available hours to paint the new designs. Additionally, because some of the machines used to make these new designs are also being used for other projects, they can make at most 12 cabinets and at most 16 end tables.
The marketing department plans to price them so that they will make $65 in profit from each cabinet and $60 for each end table. How many of each design should they make to maximize their profit?
Let x = the number of storage cabinets
Let y=the number of end tables
Use linear programming to solve. Show all your work.
a) What are the constraints for this problem? Describe what each represents.
b) What is the objective function for this problem?
c) Graph and show the feasible region with the vertices labeled.
d) Evaluate the objective function to determine the ideal number of cabinets and end tables to make.