List of top Mathematics Questions on Linear Programming Problem and its Mathematical Formulation asked in MHT CET

In a triangle ABC with usual notations if \( b \sin C (b \cos C + c \cos B) = 42 \), then area of triangle ABC =}

If a random variable $X$ follows the Binomial distribution $\text{B}(33, \text{p})$ such that $3\text{P}(\text{X} = 0) = \text{P}(\text{X} = 1)$, then the variance of X is

In a triangle ABC with usual notations, if $3a = b + c$, then $\cot \frac{B}{2} \cdot \cot \frac{C}{2} =$

The common region of the solutions of the inequations $x + 2y \ge 4$, $2x - y \le 6$ and $x, y > 0$ is

The solution set for the system of linear inequations $x+y \ge 1 ; 7x+9y \le 63 ; y \le 5 ; x \le 6, x \ge 0$ and $y \ge 0$ is represented graphically in the figure. What is the correct option?

The shaded part of the given figure indicates the feasible region. Then the constraints are

If \( Z = 7x + y \) subject to \[ 5x + y \geq 5, \quad x + y \geq 3, \quad x \geq 0, \quad y \geq 0, \quad \text{then the minimum value of } Z \text{ is} \]

The L.P.P. to maximize \( z = x + y \), subject to \[ x + y \le 30,\; x \le 15,\; y \le 20,\; x + y \ge 15,\; x \ge 0,\; y \ge 0 \] has

If \[ \int \sqrt{x - 1} \left( \frac{x^2 + 1}{x^2} \right) dx = \frac{2}{3} (x - 1)^k + c, \quad \text{then the value of } k \text{ is} \]

The order and degree of the differential equation \[ \left[ 1 + \left( \frac{dy}{dx} \right)^3 \right]^{\frac{3}{2}} = 7 \frac{d^2y}{dx^2} \] are respectively

The feasible region of the L.P.P.
\[ \text{Maximize } z = 70x + 50y \] subject to \[ 8x + 5y \le 60,\quad 4x + 5y \le 40,\quad x \ge 0,\; y \ge 0 \] is

If $Z = 10x + 25y$ subject to $0 \le x \le 3$, $0 \le y \le 3$, $x + y \le 5$, $x \ge 0$, $y \ge 0$, then $Z$ is maximum at the point

For the following shaded region, the linear constraints are:

The distance of the point \( (2, -1, 0) \) from the plane \( 2x + y + 2z + 8 = 0 \) is

The maximum value of \[ Z = 3x + 5y, \] subject to \[ x + 4y \leq 24, \quad y \leq 4, \quad x \geq 0, \quad y \geq 0 \] is

The minimum value for the LPP \( Z = 6x + 2y \), subject to \( 2x + y \geq 16, x \geq 6, y \geq 1 \) is

The maximum value of \(Z = 10x + 25y\) subject to \[ 0 \le x \le 3,\; 0 \le y \le 3,\; x + y \le 5,\; x \ge 0,\; y \ge 0 \] is