List of top Mathematics Questions on Linear Programming Problem asked in MHT CET

In triangle \( ABC \), the point \( P \) divides \( BC \) internally in the ratio \( 3 : 4 \) and \( Q \) divides \( CA \) internally in the ratio \( 5 : 3 \). If \( AP \) and \( BQ \) intersect in a point \( G \), then \( G \) divides \( AP \) internally in the ratio

If \[ x = a\cos^3\theta, \qquad y = a\sin^3\theta, \] then find \[ \sqrt{1+\left(\frac{dy}{dx}\right)^2} = \, ? \] 

In triangle \( ABC \), the point \( P \) divides \( BC \) internally in the ratio \( 3 : 4 \) and \( Q \) divides \( CA \) internally in the ratio \( 5 : 3 \). If \( AP \) and \( BQ \) intersect in a point \( G \), then \( G \) divides \( AP \) internally in the ratio
The feasible region of the linear programming problem is determined by the system of inequalities: \[ x + y \leq 6, \quad x \geq 0, \quad y \geq 0. \] What is the maximum value of \( x + y \) in the feasible region?
Maximize \( z = x + y \) subject to: \[ x + y \leq 10, \quad 3y - 2x \leq 15, \quad x \leq 6, \quad x, y \geq 0. \] Find the maximum value.
If feasible region is as shown in the figure, then the related inequalities are}
The shaded region in the following figure represents the solution set for a certain linear programming problem. Then linear constraints for this region are given by}