Intereting Posts

what numbers are integrally represented by this quartic polynomial (norm form)
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
HCF/LCM problem
Prove that an equation has no elementary solution
Why Peirce's law implies law of excluded middle?
Deriving the addition formula of $\sin u$ from a total differential equation
How prove this inequality $\sum\limits_{cyc}\frac{a^2}{b(a^2-ab+b^2)}\ge\frac{9}{a+b+c}$
Can we prove the existence of $A\cup B$ without the union axiom?
Does a continuous scalar field on a sphere have continuous loop of “isothermic antipodes”
example of a non differentiable manifold
Banach fixed-point theorem for a recursive functional equation
Condition for a ring on projective and free modules problem
sketch set satisfying $|z-2|+|z+2|\le5$
Convergence of $\sum \frac{a_n}{S_n ^{1 + \epsilon}}$ where $S_n = \sum_{i = 1} ^ n a_n$
If $\sqrt{a} + \sqrt{b}$ is rational then prove $\sqrt{a}$ and $\sqrt{b}$ are rational

Given a $m$ x $n$ matrix $A$, $m$-vectors $b$ and $y$, and $n$-vectors $c$ and $x$.

Write the dual $LP$ problems $P$ and $P^d$ in the standard form.

Whether $x$ (respectively, $y$) is a feasible vector for $P$ (respectively, for $P^d$)?

Whether x (respectively, y) is an optimal solution for $P$ (respectively, for $P^d$)?

Whether the complementary slackness conditions hold for $P$ (respectively, for $P^d$)?

- Reduced cost vector in the phase I of the Two-phase simplex?
- Prove that an edge of a polyhedron is a line segment
- Linear Programming 3 decision variables (past exam paper question)
- Why maximum/minimum of linear programming occurs at a vertex?
- minimum possible value of a linear function of n variables
- Underlying assumption in a Primal/Dual table

Consider the cases a-g listed below and explain your answers in each case.

a.) $ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, $b^T = (8,18)$, $c^T = (2,1)$, $x^T = (6,0)$, $y^T = (0,2/3)$

b.) $ A = \begin{bmatrix} 1 & 1 & 2 \\ 2 & 3 & 4 \\ 7 & 6 & 2 \end{bmatrix}$, $b^T = (2,3,8)$, $c^T = (8,9,4)$, $x^T = (6/9,5/9,0)$, $y^T = (0,5/3,2/3)$

c.) $ A = \begin{bmatrix} 1 & 1 & 2 \\ 2 & 3 & 4 \\ 6 & 6 & 2 \end{bmatrix}$, $b^T = (2,3,8)$, $c^T = (8,9,5)$, $x^T = (1,1/3,0)$, $y^T = (1,1,1)$

d.) $ A = \begin{bmatrix} 3 & 2 \\ 1 & -2 \end{bmatrix}$, $b^T = (6,1)$, $c^T = (2,1)$, $x^T = (1,2)$, $y^T = (1,1)$

e.) $ A = \begin{bmatrix} 1 & 1 & 1 & 1 \\ 2 & 1 & -1 & -1 \\ 0 & -1 & 0 & 1 \end{bmatrix}$, $b^T = (40,-5,10)$, $c^T = (1,-3,1,4)$, $x^T = (35/3,0,55/3,10)$, $y^T = (2,2,0)$

f.) $ A = \begin{bmatrix} 2 & -6 & 2 & 7 & 3 & 8 \\ -3 & -1 & 4 & -3 & 1 & 2 \\ 8 & -3 & 5& -2 & 0 & 2 \\ 4 & 0 & 8 & 7 & -1 & 3 & \\ 5 & 2 & -3 & 6 & -2 & -1\end{bmatrix}$, $b^T = (1,-2,4,1,5)$, $c^T = (18,-7,12,5,0,8)$, $x^T = (2,4,0,0,7,0)$, $y^T = (1/3,0,5/3,1,0)$

- Linear Programming with Matrix Game
- Pivoting and Simplex Algorithm
- Primal and dual solution to linear programming
- Primal- degenerate optimal, Dual - unique optimal
- Optimum solution to a Linear programming problem
- Finding nonnegative solutions to an underdetermined linear system
- How can I infer a result using primal feasibility, dual feasibility, and complementary slackness?
- Variable leaving basis in linear programming - when does it happen?

- How do you read the symbol “$\in$”?
- proving $ e^{\pi} > \pi ^{e}$
- Showing $G/Z(R(G))$ isomorphic to $Aut(R(G))$
- Visualizing $\cap_{i = 1}^\infty A_i = (\cup_{i = 1}^\infty A_i^c)^c$
- the number of Young tableaux in general
- If $A \in M_{n \times 1} (\mathbb K)$, then $AA^t$ is diagonalizable.
- Prove that $C^1_0$ with a certain metric is a complete metric space.
- Weighted Poincare Inequality
- Software for some universal algebra issues
- Prove that $\mathbb{Z}/\langle 1+i \rangle \cong \mathbb{Z}/2\mathbb{Z}$
- Asymptotics of a double integral: $ \int_0^{\infty}du\int_0^{\infty}dv\, \frac{1}{(u+v)^2}\exp\left(-\frac{x}{u+v}\right)$
- Has anybody ever considered “full derivative”?
- How to show that $\sum_{n=1}^{\infty} \frac{1}{(2n+1)(2n+2)(2n+3)}=\ln(2)-1/2$?
- Proving square root of a square is the same as absolute value
- Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.