A craftsman named William Barnes builds two kinds of birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes 4 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and 12 units of lumber. The craftsman has available 60 hours of labor and 120 units of lumber. Wren houses yield a profit of $6 each, and bluebird houses yield a profit of $15 each.
a) Write out the objective and constraints.
b) Solve graphically
Provide complete and step by step solution for the question and show calculations and use formulas.