Question

Solve the LP problem using graphical method. Determine the optimal values of the decision variables and compute the objective function.

Minimize Z = 2x1 + 3x2

Subject to

4x1 + 2x2 ≥ 20

2x1 + 6x2 ≥ 18

x1 + 2x2 ≤ 12

x1, x2 ≥ 0

with solution! thak you so much :D

Answer #1

a. Solve the following linear programming model by using the
graphical method: graph the constraints and identify the feasible
region then determine the optimal solution (s) (show your
work).
Minimize Z = 3x1 + 7x2
Subject to 9x1 + 3x2 ≥ 36
4x1 + 5x2 ≥ 40
x1 – x2 ≤ 0
2x1 ≤ 13
x1, x2 ≥ 0
b. Are any constraints binding? If so, which one (s)?

Using the graphical method, described in class, determine the
optimal
solution(s) (if they exist) for the linear program. If no optimal
exists, then indicate
that and explain why no optimal solution exists.
(a)
Maximize : z = 2x1 + 8x2
Subject to :
3x1 ≤ 12
x1 + 4x2 ≤ 24
x1 ≥ 0
x2 ≥ 0
(b)
Maximize : z = 2x1 − 3x2
Subject to :
6x1 − 3x2 ≤ −9
x1 ≤ 0
x2 ≤ 0

Solve The LP problem using the graphic method
Z Max=5X1+3X2
Constaint function:
2X1 + 4X2 ≤ 80
5X1 + 2X2 ≤ 80
X1≥ 0 , X2≥0

Solve The LP problem using the graphic method
Z Max=15X1+10X2
Constaint function:
3X1 + 2X2 ≤ 80
2X1 + 3X2 ≤ 70
X1≥ 0 , X2≥0

max Z = 5x1+3x2+x3
s.t : 2x1+x2+x3 < 6
x1+2x2+x3 < 7
x1, x2, x3 > 0
Solve the problem. What is the optimal value of the objective
function (OF)? Decision variables?
Solve the problem. What is the optimal value of the objective
function (OF)? Decision variables?
(20 points)

Solve the following linear programming model by using the
graphical method: graph the constraints and identify the feasible
region. Using the corner points method, determine the optimal
solution (s) (show your work).
Maximize Z = 6.5x1 + 10x2
Subject to x1 + x2 ≤ 15
2x1 + 4x2 ≤ 40
x1 ≥ 8
x1, x2 ≥ 0
b. If the constraint x1 ≥ 8 is changed to x1 ≤ 8, what effect
does this have on the optimal solution? Are...

Solve the following LP model using the dual simplex method. Use
the format of the tabular form of the simplex without converting
the problem into a maximization problem.
Minimize -2x1 – x2
Subject to
x1+ x2+ x3 = 2
x1 + x4 = 1
x1, x2, x3, x4 ³ 0

3) Find the dual of the following LP: Max 4x1 - x2 s.t. 2x1 +
3x2 ≥ 10 x1 – x2 = 4 0.5x1 + 2x2 ≤ 20 x1 ≥ 0, x2 unconstrained
Please provide an excel solution to this problem

Solve the following linear program using the simplex method. If
the problem is two dimensional, graph the feasible region, and
outline the progress of the algorithm.
Minimize Z = 3X1 – 2X2 – X3
Subject to 4X1 + 5X2 – 2X3 ≤
22
X1 – 2X2 + X3 ≤ 30
X1, X2, X3 ≥ 0

Solve The LP problem using the graphic method
Z Max=6X1+5X2
Constaint function:
X1 + 2X2 ≤ 240
3X1 + 2X2 ≤ 300
X1≥ 0 , X2≥0

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