Convert to standard
maximum form and apply two iterations of simplex process using
slack form.
Maximize
2x1 -6x3
Subject to
x1 + x2 – x3 <=
7
3x1 – x2 >= 8
-x1 + 2x2 + 2x3
>= -2
x2, x3 >=0
Please write the answer very clearly.
Maximization by the simplex method
Solve the following linear programming problems using the
simplex method.
1>.
Maximize z = x1 + 2x2 +
3x3
subject to x1 + x2 +
x3 ≤ 12
2x1 + x2 + 3x3 ≤ 18
x1, x2, x3 ≥ 0
2>.
A farmer has 100 acres of land on which she plans to grow wheat
and corn. Each acre of wheat requires 4 hours of labor and $20 of
capital, and each acre of corn...
Write a function to solve a system of linear equations of the
form Ax= b using the iterative Gauss-Seidel
method. You are free to use any basic MATLAB operation to implement
the algorithm (i.e. you may use any combination of loops, indexing,
math, etc.), but avoid “built-in” solution methods — you would not
be allowed to use the GaussSeidel
function if such a function existed. The function must also
test for a number of possible issues. If an issue is...
Find the objective function and the constraints, and then solve
the problem by using the simplex method. A confectioner has 600
pounds of chocolate, 100 pounds of nuts, and 50 pounds of fruits in
inventory with which to make three types of candy: Sweet Tooth,
Sugar Dandy, and Dandy Delite. A box of Sweet Tooth uses 3 pounds
of chocolate, 1 pound of nuts, and 1 pound of fruit and sells for
$8. A box of Sugar Dandy requires 4...
1) Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express your answer in terms
of the parameters t and/or s.)
3y
+
2z
=
1
2x
−
y
−
3z
=
4
2x
+
2y
−
z
=
5
(x, y, z)
=
2) Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION....
Solve the following problem using the simplex method. If the
problem is two dimensional, graph the feasible region, and outline
the progress of the algorithm.
Max
Z = 5X1 + 3X2 +
2X3
Subject to 4X1 + 5X2 +
2X3 + X4≤ 20
3X1 + 4X2 - X3 + X4≤ 30
X1, X2, X3, X4 ≥
0
Use the simplex method to solve the following problem. Find y1 ≥
0, y2 ≥ 0, and y3 ≥ 0 such that
2 y1 + 7 y2 + 3 y3 ≤ 11,
2 y1 + 14 y2 + 8 y3 ≥ 1010,
and
w = 12 y1 + 42 y2 + 59 y3 is minimized.
The minimum value w = ___ occurs when y1 = ___, y2 = ___, and
y3 = ___.
(Simplify your answers.)