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 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 for $50 and her vases for 40$ .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 branch and bound method .compare this solution with the solution with integer restrictions and indicate if the rounded-down split would have been optimal