Question

Solve The LP problem using the graphic method

Z Max=15X_{1}+10X_{2}

Constaint function:

3X_{1} + 2X_{2} ≤ 80

2X_{1} + 3X_{2} ≤ 70

X_{1}≥ 0 , X_{2}≥0

Answer #1

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=6X1+5X2
Constaint function:
X1 + 2X2 ≤ 240
3X1 + 2X2 ≤ 300
X1≥ 0 , X2≥0

Consider the following LP problem:
Minimize Cost = 3x1 +
2x2
s.t.
1x1 + 2x2 ≤ 12
2x1 + 3 x2 = 12
2 x1 + x2 ≥ 8
x1≥ 0,
x2 ≥ 0
What is the optimal solution of this LP?
(0,8)(12,0)(4,0)(0,4)(2,3)(0,6)(3,2)
I NEED SOLUTION!

Duality Theory: Consider the following LP:
max 2x1+2x2+4x3
x1−2x2+2x3≤−1
3x1−2x2+4x3≤−3
x1,x2,x3≤0
Formulate a dual of this linear program. Select all the correct
objective function and constraints
1. min −y1−3y2
2. min −y1−3y2
3. y1+3y2≤2
4. −2y1−2y2≤2
5. 2y1+4y2≤4
6. y1,y2≤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 LP problem graphically using level
curves.
MAX: 7 X1 + 4 X2
Subject to: 2X1 + X2 ≤ 16
X1 + X2 ≤ 10
2X1 + 5 X2 ≤ 40
X1, X2 ≥ 0
a. X1 = 4
b. X1 = 6
c. X1 = 8
d. X1 = 10

Given a LP model as:Minimize Z = 2X1+ 4X2+ 6X3
Subject to:
X1+2X2+ X3≥2
X1–X3≥1
X2+X3= 1
2X1+ X2≤3
X2, X3 ≥0, X1 urs
a) Find the standard form of the LP problem.
b) Find the starting tableau to solve the Primal LP problem by
using the M-Technique.

Solve the LPP below by making use of the dual simplex
method.
min z=2x1+3x2+4x3
st: x1+2x2+x3>=3
2x1-x2+3x3>=4
x1,x2,x3>=0

Find the duals of the following LP:
max z = 4x1 - x2 + 2x3
s.t. x1 + x2 <= 5
2x1 + x2 <= 7
2x2 + x3 >= 6
x1 + x3 = 4
x1 >=0, x2, x3 urs
show steps

Solve the following LP problem graphically; confirm your results
using Solver in MS Excel. Maximize profit = 20x1 + 10x2 Subject to:
5x1 + 4x2 ≤ 250 2x1 + 5x2 ≤ 150 x1, x2 ≥ 0

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