1.Use branch-and-bound to solve the following IP problem.
This problem must be solved in graphical approach.
Max Z = 5X1 + 2X2
S.T.
3X1 + X2 <= 12
X1 + X2 <=5
X1 >= 0, X2>=0
X1 and X2 are integer
2 - A manufacturer can sell product 1 at a profit of $2/unit and product 2 at a profit of $5/unit. Three units of raw material are needed to manufacture 1 unit of product 1, and 6 units of raw material are needed to manufacture one unit of product 2. A total of 120 units of raw material are available. If any of product 1 is produced, a set up cost of $10 is incurred, and if any of product 2 is produced, a setup cost of $20 is incurred. Formulate an IP to maximize profits (only formulation. Do not solve).