# Recent questions and answers in Optimization

1
Consider the following linear programming (LP): $\begin{array}{ll} \text{Max.} & z=2x_1+3x_2 \\ \text{Such that} & 2x_1+x_2 \leq 4 \\ & x_1 + 2x_2 \leq 5 \\ & x_1, x_2 \geq 0 \end{array}$ The optimum value of the LP is $23$ $9.5$ $13$ $8$
2
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
3
Bounded minimalization is a technique for proving whether a promotive recursive function is turning computable or not proving whether a primitive recursive function is a total function or not generating primitive recursive functions generating partial recursive functions
4
Consider the following transportation problem: The initial basic feasible solution of the above transportation problem using Vogel's Approximation method (VAM) is given below: The solution of the above problem: is degenerate solution is optimum solution needs to improve is infeasible solution
1 vote
5
The initial basic feasible solution of the following transportion problem: is given as 5 8 7 2 2 10 then the minimum cost is 76 78 80 82
1 vote
6
The initial basic feasible solution to the following transportation problem using Vogel's approximation method is $\begin{array}{|c|c|c|c|c|c|} \hline \text{} & \textbf{$D_1$} & \textbf{$D_2$} & \text{$D_3$} & \text{$D_4$} & \textbf{Supply} \\\hline \textbf{$ ... = 180 $x_{11}=20, x_{13}=10, x_{22}=20, x_{23}=20, x_{24}=10, x_{32}=10$, Total cost = 180 None of the above
7
In constraint satisfaction problem, constraints can be stated as Arithmetic equations and inequalities that bind the values of variables Arithmetic equations and inequalities that does not bind any restriction over variables Arithmetic equations that impose restrictions over variables Arithmetic equations that discard constraints over the given variables
8
Consider the following transportation problem: The transportation cost in the initial basic feasible solution of the above transportation problem using Vogel's Approximation method is $1450$ $1465$ $1480$ $1520$
1 vote
9
A basic feasible solution of a linear programming problem is said to be ______ if at least one of the basic variable is zero generate degenerate infeasible unbounded
10
Consider the following conditions: The solution must be feasible, i.e. it must satisfy all the supply and demand constraints The number of positive allocations must be equal to $m+n-1$, where $m$ is the number of rows and $n$ is the number of columns All the positive allocations must be in independent ... solution if it satisfies: $a$ and $b$ only $a$ and $c$ only $b$ and $c$ only $a$, $b$ and $c$
11
Given the following statements with respect to linear programming problem: S1: The dual of the dual linear programming problem is again the primal problem S2: If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution S3: If ... the two problems are equal. Which of the following is true? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
12
In the Hungarian method for solving assignment problem, an optimal assignment requires that the maximum number of lines that can be drawn through squares with zero opportunity cost be equal to the number of rows or columns rows + columns rows + columns -1 rows + columns +1
13
Given the problem to maximize $f(x), X=(x_1, x_2, \dots , x_n)$ subject to m number of in equality constraints. $g_i(x) \leq b_i$, i=1, 2, .... m including the non-negativity constrains $x \geq 0$ ... $g_i (\bar{X}) \leq b_i, i=1,2 \dots m$ All of these
14
The following Linear Programming problem has: $\text{Max} \quad Z=x_1+x_2$ Subject to $\quad x_1-x_2 \geq 0$ $\quad \quad \quad 3x_1 - x_2 \leq -3$ $\text{and} \quad x_1 , x_2 \geq 0$ Feasible solution No feasible solution Unbounded solution Single point as solution
15
If the primal Linear Programming problem has unbounded solution, then it's dual problem will have feasible solution alternative solution no feasible solution at all no alternative solution at all
1 vote
16
Which of the following special cases does not require reformulation of the problem in order to obtain a solution ? Alternate optimality Infeasibility Unboundedness All of the above
The feasible region represented by the constraints $x_1 - x_2 \leq 1, x_1 + x_2 \geq 3, x_1 \geq 0, x_2 \geq 0$ of the objective function Max $Z=3x_1 + 2x_2$ is A polygon Unbounded feasible region A point None of these