Question: (10 pts) A furniture company produces desks and bookcases from two resources – wood and labor. Each desk requires 7.5 hours of labor and 3 pounds of wood. Each bookcase requires 3 hours of labor and 5 pounds of wood. The profit for each desk is $50 and $40 for each bookcase. The company has 150 pounds of wood and 150 hrs of labor available each day. The company wants to know the number (integer) of desks and bookcases to produce each day in order to maximize profit.

a. Formulate a linear programming model for this problem.

b. Solve using the computer. Compare the solution with the solution without integer restrictions (real) and indicate whether the rounded-down solution would have been optimal.