Recent questions tagged linear-programming

1
Consider the following LPP: $\begin{array}{ll} \text{Min.} Z= & x_{1}+x_{2}+x_{3} \\ \text{Subject to } & 3x_{1}+4x_{3}\leq 5 \\ & 5x_{1}+x_{2}+6x_{3}=7 \\ & 8x_{1}+9x_{3}\geq 2, \\ &x_{1},x_{2},x_{3} \geq 0 \end{array}$ ...
1 vote
2
The following LLP $\text{Maximize } z=100x_1 +2x_2+5x_3$ Subject to $14x_1+x_2-6x_33+3x_4=7$ $32x_1+x_2-12x_3 \leq 10$ $3x_1-x_2-x_3 \leq 0$ $x_1, x_2, x_3, x_4 \geq 0$ has Solution : $x_1=100, \: x_2=0, \: x_3=0$ Unbounded solution No solution Solution : $x_1=50, \: x_2=70, \: x_3=60$
3
The following table gives the cost of transporting one tonne of goods from the origins A, B, C to the destinations F, G, H. Also shown are the availabilities of the goods at the origins and the requirements at the destinations. The transportation problem implied by ... question(i). For the solution of (ii) above, calculate the values of the duals and determine whether this is an optimal solution.
1 vote
4
If the transportation problem is solved using some version of the simplex algorithm, under what condition will the solution always have integer values?
1 vote
5
Fill in the blanks: The solution to the following linear program $\max$ $X_{1}$ such that $X_{1}+2X_{2} \leq 10$ $X_{1} \leq 8$ $X_{1} \leq 1$ is ____________.
6
Consider the following statements : (a) Assignment problem can be used to minimize the cost. (b) Assignment problem is a special case of transportation problem. (c) Assignment problem requires that only one activity be assigned to each resource. Which of the following options is correct ? (a) and (b) only (a) and (c) only (b) and (c) only (a), (b) and (c)
1 vote
7
Consider the following statements : (a) If primal (dual) problem has a finite optimal solution, then its dual (primal) problem has a finite optimal solution. (b) If primal (dual) problem has an unbounded optimum solution, then its dual (primal) has no feasible solution at all. (c) Both primal and dual ... following is correct ? (a) and (b) only (a) and (c) only (b) and (c) only (a), (b) and (c)
8
Consider the following linear programming problem : $\max. z = 0.50 x_{2} – 0.10x_{1}$ Subject to the constraints $2x_{1} + 5x_{2} \leq 80$ $x_{1} + x_{2} \leq 20$ and $x_{1}, x_{2} \geq 0$ The total maximum profit $(z)$ for the above problem is : $6$ $8$ $10$ $12$
9
The region of feasible solution of a linear programminig problem has a ____ property in geometry, provided the feasible solution of the problem exists concavity convexity quadratic polyhedron
1 vote
10
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
1 vote
11
If an artificial variable is present in the ‘basic variable’ column of optimal simplex table, then the solution is Optimum Infeasible Unbounded Degenerate
12
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
13
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
14
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
1 vote
15
If an artificial variable is present in the ‘basic variable’ of optimal simplex table then the solution is Alternative solution Infeasible solution Unbounded solution Degenerate solution
1 vote
16
The total transportation cost in an initial basic feasible solution to the following transportation problem using Vogel's Approximation method is W1 W2 W3 W4 W5 W6 F1 4 2 3 2 6 8 F2 5 4 5 2 1 12 F3 6 5 4 7 3 14 Demand 4 4 6 8 8 $\begin{array}{|l|l|l|l|} \hline \text{} & \text{$ ... 76 80 90 96
17
A basic feasible solution to a m-origin, n-destination transportation problem is said to be ______ if the number of positive allocations are less than m+n-1. degenerate non- degenerate unbounded unbalanced
18
At any iteration of simplex method if $\Delta j (Zj &ndash; Cj)$ corresponding to any non-basic variable $Xj$ is obtained as zero, the solution under the test is Degenerate solution Unbounded solution Alternative solution Optimal solution
1 vote
19
In a Linear Programming Problem, suppose there are three basic variables and 2 non-basic variables, then the possible number of basic solutions are 6 8 10 12
20
Consider the statement "Either $-2 \leq x \leq -1 \text{ or } 1 \leq x \leq 2$" The negation of this statement is x<-2 or 2<x or -1<x<1 x<-2 or 2<x -1<x<1 x $\leq$ -2 or 2 $\leq$ x or -1<x<1
In any simplex table, if corresponding to any negative $\Delta$ j, all elements of the column are negative or zero, the solution under the test is degenerate solution unbounded solution alternative solution non-existing solution
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