Helen Holmes makes pottery by hand in her basement. She has 20 hours available each week to make bowls and vases. A bowl requires 3 hours of labor, and a vase requires 2 hours of labor. It requires 2 pounds of special clay to make a bowl and 5 pounds to produce a vase; she is able to acquire 35 pounds of clay per week. She sells her bowls for50andhervasesfor40. She wants to know how many of each item to make each week in order to maximize her revenue.

a. Formulate an integer programming model for this problem.

b. Solve this model using the branch and bound method. Compare this solution with the solution without integer restrictions and indicate if the rounded-down solution would have been optimal.