List of top Mathematics Questions on Linear Programming Problem and its Mathematical Formulation

If the system of linear equations \(x - 2y + z = -4\); \(2x + αy + 3z = 5\) and \(3x - y + βz = 3\) has infinitely many solutions then \(12α + 13β\) is equal to

Consider the Linear Programming Problem:
Minimize 3x₁+4x₂ +2x₃
subject to
x₁+x₂+x₃≤6
x₁+2x₂+x₃≤10
x₁,x₂,x₃≥0.
Then, the number of basic solutions are

Which of the following is the correct formulation of the linear programming problem ?

Consider the following Linear Programming Problem(LPP):Maximize \(z=60x_1+50x_2\) subject to \(x_1+2x_2≤40 3x_1+2x_2≤60 x_1,x_2≥0\).Then, the ______.

If the system of linear equations.
\(8x + y + 4z = –2\)
\(x + y + z = 0\)
\(λx–3y=μ\)
has infinitely many solutions, then the distance of the point \((λ, μ, -1/2)\) from the plane \(8x + y + 4z + 2 = 0\) is

The distance of the point whose position vector is \(\mathbf{2\hat{i} + \hat{j} - \hat{k}}\) from the plane vector \(\vec{r} \cdot (\hat{i} - 2\hat{j} + 4\hat{k}) = 4\) is

Find the mean number of heads in three tosses of fair coin:

Corner points of the feasible region determined by the system of linear constraints are $(0, 3), (1, 1)$ and $(3, 0)$. Let $z = px = qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the minimum of $z$ occurs at $(3, 0)$ and $(1, 1)$ is

The feasible region of an LPP is shown in the figure. If $Z = 11x + 7y$, then the maximum value of $Z$ occurs at

The feasible region of an LPP is shown in the figure. If Z = 11x + 7y then the maximum value of Z occurs at

If the constraints in a linear programming problem are changed then

Minimise $Z=\displaystyle\sum_{j=1}^{n} \displaystyle\sum_{i=1}^{m} c_{i j} \cdot x_{i j}$ Subject to $\displaystyle\sum_{ i =1}^{ m } x _{ ij }= b _{ j }, j =1,2, \ldots \ldots n$ $\displaystyle\sum_{j=1}^{n} x_{i j}=b_{j}, j=1,2, \ldots \ldots, m$ is a LPP with number of constraints

The optimal value of the objective function is attained at the points

To maximize the objective function $z = 2x + 3y $ under the constraints $x + y \leq 30, x - y \geq 0 , y \leq 12, x \leq 20 , y \geq 3$ and $x ,y \geq 0 $

The intermediate solutions of constraints must be checked by substituting them back into

The corner points of the feasible region determined by the system of linear constraints are $(0,0), (0,40), (20, 40), (60, 20), (60, 0)$. The objective function is $Z = 4x + 3y$. Compare the quantity in Column $A$ and Column $B$