Question

Determine whether or not constraint qualification is satisfied as the optimum X* for the following problem:

Maximize X_{1}

Subject to:

(X_{1} -1)^{3} + (X_{2} -2) ≤ 0

(X_{1} -1)^{3} - (X_{2} -2) ≤ 0

X_{1}, X_{2} ≥ 0

Answer #1

Determine if completeness and transitivity are satisfied for the
following preferences defined on x = (x1, x2) and y = (y1, y2).
(Hints: 1- You have to use z = (z1, z2) to prove or disprove
transitivity. 2- You can disprove by a counter example) — x ≽y iff
x1 > y1 or x1 = y1 and x2 > y2.

Determine if completeness and transitivity are satisfied for the
following preferences defined on x = (x1, x2) and y = (y1, y2).
(Hints: 1- You have to use z = (z1, z2) to prove or disprove
transitivity. 2- You can disprove by a counter example) — x ≽y iff
x1 > y1 or x1 = y1 and x2 > y2.

Determine if completeness and transitivity are satisfied for the
following preferences defined on x = (x1, x2) and y = (y1, y2).
(Hints: 1- You have to use z = (z1, z2) to prove or disprove
transitivity. 2- You can disprove by a counter example) — x ≽y iff
x1 > y1 or x1 = y1 and x2 > y2.

Determine if completeness and transitivity are satisfied for the
following preferences defined on x = (x1, x2)
and y = (y1, y2).
x ≽ y iff x1 > y1 or
x1 = y1 and x2 >
y2.
(Hints: 1- You have to use z = (z1, z2) to
prove or disprove transitivity. 2- You can disprove by a counter
example)

Consider the following linear programming problem
Maximize
$1 X1 + $3 X2
Subject To
X1 + X2 ≤ 4
Constraint A
X1 - X2 ≤ 1
Constraint B
X1, X2 ≥ 0
Constraint C
Note: Report two digits after the decimal point. Do NOT
use thousands-separators (,)
1 - Which of the following is the correct standard maximization
form for the above linear programming problem
Answer CorrectNot Correct
Answer CorrectNot Correct
Answer CorrectNot Correct
Answer CorrectNot Correct
Z - X1...

The following is the mathematical model of a linear programming
problem for profit:
Maximize Z = 2X1 + 3X2
subject to:
4X1 + 9X2 ≤ 72
10X1 + 11X2 ≤ 110
17X1 + 9X2 ≤ 153
X1 , X2 ≥ 0
The constraint lines have been graphed below along with one example
profit line (dashed). The decision variable X1 is used as the X
axis of the graph.
Which of the following gives the constraint line that cuts the
X2...

Find the maximum and minimum values of the following function,
subject to the given constraint. Maximize and minimize the function
f(x, y) = xy2 subject to the constraint x2 + y2 = 1.
maximum of ____at (x, y) = (____,_____)
minimum of _____ at (x, y) = (_____,____)

Consider the following problem.
Maximize Z = 2x1 -
x2 + x3,
subject to
x1 -
x2 + 3x3 ≤ 4
2x1 +
x2
≤ 10
x1 - x2 -
x3 ≤ 7
and x1 ≥
0, x2 ≥ 0,
x3 ≥ 0.
Use Excel Solver to solve this problem.
Write out the augmented form of this problem by introducing
slack variables.
Work through the simplex method step by step in tabular form to
solve the problem.

The following is the mathematical model of a linear programming
problem for profit:
Maximize subject to
Z = 2X1 + 3X2
4X1+9X2 ≤ 72 10X1 + 11X2 ≤ 110 17X1 + 9X2 ≤ 153
X1 , X2 ≥ 0
The constraint lines have been graphed below along with one
example profit line (dashed). The decision variable X1 is used as
the X axis of the graph. Use this information for questions
19 through 23.
A). Which of the following gives...

Maximize 12X1 + 10X2 + 8X3
Total Profit
Subject to X1 + X2 + X3 >
160 At least a total of
160 units of all three products needed
X1
+ 3X2 + 2X3 ≤ 450
Resource 1
2X1 + X2 +
2X3 ≤ 300 Resource
2
2X1 + 2X2 + 3X3 ≤
400 Resource 3
And X1,
X2, X3 ≥ 0
Where X1, X2, and X3 represent the number of units of Product 1,
Product...

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