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...
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.
Given the following primal problem:
maximize z = 2x1 + 4x2 + 3x3
subject to
x1 + 3x2 + 2x3 ≥ 20
x1 + 5x2 ≥ 10
x1 + 2x2 + x3 ≤ 18
x1 , x2 , x3 ≥ 0
1. Write this LP in standart form of
LP.
2.Find the optimal solution to
this problem by applying the Dual Simplex method
for finding the initial basic feasible solution to the
primal of this LP. Then, find the optimal...
Max Z = 2x1 + 8x2 + 4x3
subject to
2x1 + 3x2 ≤ 8
2x2 + 5x3 ≤ 12
3x1 + x2 +
4x3
≤15
and x1,x2,x3≥0;
Indicate clearly the optimal basic and nonbasic
variables and their values and write the reduced cost of each
optimal nonbasic variable.
For the following linear programming problem:
Maximize z = 2x1+ x2
Such that
x1+ 2x2 ≤ 12
x2 ≥
3
x1,x2 ≥
0
(a) Write the first two constraints in equation form by adding
slack or subtracting excess (surplus) variables.
(b)Find all basic solutions for this LP
(c) Which of these solutions are feasible?
(d)Which of these feasible solutions is optimal? Find the
optimal value of z