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A craftsman builds 2 kinds of birdhouses, 1 for swallows (X1), 1 for bluebirds (X2). Each swallow birdhouse takes 4 hours of labor \& 4 units of lumber. Each bluebird house takes 2 hours of labor \& 12 units of lumber. The craftsman has available 60 hours of labor \& 120 units of lumber. Swallow houses profit $6 each and bluebird houses profit $15 each. (a) Formulate the problem's objective function and constraints. (b) Graphically represent the constraints and define the location of the feasible region. (c) Find the optimal solution using the corner point method