Exercise no 1 Given the following problem of PL:

min x₂

s.a

x₂ 2

x₁x₂ 1

1. draw the eligible region P 2. for each vertices identified, indicate which constraints it activates.

3. if it exists, indicate the optimal solution,

4. verify by Simplest Method the answer to point 3.

What would have happened if the obicitive function had been

Exercise no 2 Given the following problem of PL:

min x₁

s.a

x₁ - x₂ > 0

x₂ > 1

x₁, x₂ >1

1. draw the eligible region P. 2. for each identified vertex indicate which constraints it activates.

3. if it exists, indicate the optimal solution. 4. verify by Simplesso Method the answer to point 3.

What would have happened if the target function had been max

max x₁-x₂ ?

Exercise 3

Describe and comment on the procedure to obtain an eligible basic solution for a PL Problem.

Exercise 4

The Problem of the Minimum Coverage Tree is described, also reporting the logical-mate mat model.

Exercise 5

A) Solve the Problem of the 0/1 Backpack characterized by a backpack with a capacity of 23 Kg, and 1 item whose

Weights and profits are shown in the table below:

Item	Weight (KG)	Profit (Euro)
1	10	11
2	8	7
3	6	1
4	9	9

(B) The stop conditions of the algorithm used are reported in point (a).

Exercise 6

Please report and comment on the mathematical model of the Transport Problem.