A builder specializes in the construction of car garages and tool sheds. It has at most 80 hours available to frame the garages and tool sheds and at most 74 hours to roof the garages and tool sheds. It takes 10 hours to frame a garage and 7 hours to roof it. It takes 4 hours to frame a tool shed and 5 hours to roof it. If the builder makes a profit of $570 per garage and $300 per tool shed, how many can he build to receive a maximum profit? Do the following: 1. Formulate the builder's decision as a linear program. You do not need to solve the program. 2. Sketch the feasible set. Be sure to label the axes carefully. On the graph, circle any point corresponding to values of the choice variables that you think are likely to be optimal.