(a) By branching on x ₂ , use the branch-and-bound method to solve the following integer programming problem (IP): 

Maximize z 6x ₁ + 2x ₂  

Subject to 

5x ₁ + x ₂ ≤ 10 

2x ₁ +x ₂ ≤ 9 

x ₁ . x ₂   ≥ 2 0; x ₁ , x ₂ integer. 

b) A hiker has a 5-ft backpack and needs to decide on the most valuable items to take on the hiking trip. There are three items from which to choose. Their volumes are 2, 3, and 4 ft ^3,  and the hiker estimates their associated values on a scale from 0 to 100 as 30, 50, and 70, respectively. Formulate the problem as an LP model and what kind of linear programming is it?