PROBLEM 1.
Solve the Integer Linear Programming Problem:
Max {z = 7x + 3y}, subject to constraints:
2x + 5y ≤ 28; 8x + 3y ≤ 48; x, y - non-negative integers.
Submit both graphical solution and solution by LINGO software.
PROBLEM 2.
The vector X = (2, 0, 4) is the optimal solution of the Linear Programming Problem:
Max {z = 4x1 + 2x2 + 3x3}, subject to constraints:
2x1 + 3x2 + x3 ≤ 12; x1 + 4x2 + 2x3 ≤ 10; 3x1 + x2 + x3 ≤ 10; x1, x2, x3 ≥ 0.
Solve the dual problem using the Duality Theory in Linear Programming.