Solve the following linear programming model graphically:
Max Z= 3x1 +4x2
Subject to: 2x1 + 4x2 <= 22
-x1 + 4x2 <= 10
4x1 – 2x2 <= 14 x1 – 3x2 <= 1
x1, x2, >=0
Clearly identify the feasible region, YOUR iso-profit line and
the optimal solution (that is, d.v. values and O.F. Value.
Consider the following linear programming problem.
min −x1 + 4x2
subject to:
• x1 + x2 ≥ 1
• 3x1 + x2 ≤ .5
• x1, x2 ≥ 0
Formulate the dual of this problem.
Consider the following all-integer linear program:
Max
x1 + x2
s.t.
4x1 + 6x2 ≤ 22
x1 + 5x2 ≤ 15
2x1 + x2 ≤ 9
x1, x2 ≥ 0
and integer
Solve the LP Relaxation of this problem.
The optimal solution to the LP Relaxation is x1
= ___, x2 = .____________
Its value is ___________
Find the optimal integer solution.
The optimal solution to the LP Relaxation is x1
= _____x2 = __________
Its value is _______
Consider the following linear program:
maximize z = x1 + 4x2 subject to: x1 + 2x2 <= 13 x1 - x2 <= 8
- x1 + x2 <= 2
-3 <= x1 <= 8 -5 <= x2 <= 4
Starting with x1 and x2 nonbasic at their lower bounds, perform ONE
iteration of the Bounded Variables Revised Simplex Method. (Tableau
or matrix form is acceptable). Show your work. Clearly identify the
entering and leaving variables. After the pivot, identify the...