Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 2x2 + 3x3
Subject to:
0x1 + 6x2 + 2x3 >= J
3x1 + 2x3 + 5x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 25
K = 24
Please do on paper...
Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 2x2 + 3x3
Subject to:
0x1 + 6x2 + 2x3 >= J
3x1 + 2x3 + 5x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 25
K = 24
Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 1x2 + 2x3
Subject to:
2x1 + 2x2 + 1x3 >= J
5x1 + 6x2 + 7x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 15
K = 17
Please do on paper..
Write the dual maximization problem, and then solve both the
primal and dual problems with the simplex method. (For the dual
problem, use x1, x2, and x3 as the variables and f as the
function.) Minimize g = 6y1 + 28y2 subject to 2y1 + y2 ≥ 14 y1 +
3y2 ≥ 14 y1 + 4y2 ≥ 17 . primal g = primal y1 = primal y2 = dual f
= dual x1 = dual x2 = dual x3 =
Solve the following linear programming problem. You must
use the dual. First write down the dual maximization LP problem,
solve that, then state the solution to the original minimization
problem.
(a) Minimize w = 4y1 +
5y2 + 7y3
Subject to: y1 + y2 + y3 ≥
18
2y1 + y2 + 2y3 ≥ 20
y1 + 2y2 + 3y3 ≥ 25
y1, y2, y3 ≥ 0
(b) Making use of shadow costs, if the
2nd original constraint changed to...
Consider the LP problem below: Minimize: ? = −2? + ? Subject
to:
3? + 4? ≤ 80 −3? + 4? ≥ 8 ? + 4? ≥ 40
a) Solve the above problem using the simplex method of
solution.
b) Comment on the nature of solution to the above problem and
hence, interpret your answer
this is a quantitative method for decidion making question. Linear
programing problems using simplex tableau method