Question

Given are V : 2x_{1} + 2x_{2} −x_{3} = 5
and W : x_{1} −x_{3} = 0.

1. Calculate the angle between V and W

2. Determine, independent of each other, the equation of a
paramater representation of the surface perpendicular on V and W
through point (1,2,2)

Answer #1

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.

Consider the following
LP: Max Z=X1+5X2+3X3
s.t. X1+2X2+X3=3
2X1-X2 =4 X1,X2,X3≥0
a.) Write the associated dual model
b.) Given the information that the optimal basic variables are
X1 and X3, determine the associated optimal dual solution.

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)

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

Consider the following system of linear equations:
2x1−2x2+4x3
=
−10
x1+x2−2x3
=
5
−2x1+x3
=
−2
Let A be the coefficient matrix and X the solution matrix to the
system. Solve the system by first computing A−1 and then
using it to find X.
You can resize a matrix (when appropriate) by clicking and dragging
the bottom-right corner of the matrix.

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

Consider the following system of equations.
x1- x2+ 3x3 =2
2x1+ x2+ 2x3 =2
-2x1 -2x2 +x3 =3
Write a matrix equation that is equivalent to the system of
linear equations.
(b) Solve the system using the inverse of the coefficient
matrix.

Consider the following system of equations.
x1+2x2+2x3 −
2x4+2x5 = 5
−2x1 − 4x3+ x4 −
10x5 = −11
x1+2x2 − x3+3x5 =
4
1. Represent the system as an augmented matrix.
2. Reduce the matrix to row reduced echelon form. (This can be
accomplished by hand or by MATLAB. No need to post code.)
3. Write the set of solutions as a linear combination of vectors
in R5. (This must be accomplished by hand using the rref
form found...

Use Gaussian elimination to solve the following system of linear
equations.
2x1 -2x2 -x3
+6x4 -2x5=1
x1 - x2
+x3 +2x4 - x5=
2
4x1 -4x2
-5x3 +7x4
-x5=6

Consider the problem max 4x1 + 2x2 s.t. x1 + 3x2 ≤ 5 (K) 2x1 +
8x2 ≤ 12 (N) x1 ≥ 0, x2 ≥ 0 and the following possible market
equilibria: i) x1 = 0, x2 = 3/2, pK = 0, pN = 1/4, ii) x1 = 1, x2 =
2, pK = 2, pN = 1, iii) x1 = 1, x2 = 2, pK = 4, pN = 0, iv) x1 = 5,
x2 = 0, pK =...

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