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 $72$ 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. The aim of the objective function for William should be to the objective value. Decision variables: X $=$ number of wren houses to be produced Y $=$ number of bluebird houses to be produced