Assignment Ch3
1.
Max Z = 2𝑥𝑥1 𝑥𝑥2 + 𝑥𝑥1
subject to:
𝑥𝑥12 + 𝑥𝑥2 ≤ 20
𝑘𝑘𝑥𝑥1 − 𝑥𝑥2 ≤ 5 , 𝑘𝑘 = uniform(0,1)
𝑥𝑥1 ∈ {0,1}, 𝑥𝑥2 is an integer value
If the above mathematical model is a linear programming model, please
specify which basic assumptions of linear programming are violated and why they
are violated.
2. Use the graphical approach to sketch the feasible region for the following problem.
s.t.
Max Z = 4𝑥𝑥1 + 5𝑥𝑥2
𝑥𝑥1 + 2𝑥𝑥2 ≤ 10
𝑥𝑥1 + 𝑥𝑥2 ≤ 6
𝑥𝑥1 ≤ 4
𝑥𝑥1 , 𝑥𝑥2 ≥ 0
3. For the problem 2,
(1) Use the extreme-point approach (CPF approach) to find the optimal solution
and the optimal objective value.
(2) Use the objective function approach (iso-profit line approach) to find the
optimal solution and the objective value.
4. Textbook Problem 3.1-10
5. Textbook Problem 3.4-7 (a)
6. Textbook Problem 3.4-8 (a)
7. Textbook Problem 3.4-14(a)