List of top Mathematics Questions on Linear Programming asked in CBSE CLASS XII, CBSE Compartment XII

Solve the following LPP graphically: Maximize: \[ Z = 2x + 3y \] Subject to: \[ \begin{aligned} x + 4y &\leq 8 \quad \text{(1)} \\ 2x + 3y &\leq 12 \quad \text{(2)} \\ 3x + y &\leq 9 \quad \text{(3)} \\ x &\geq 0,\quad y \geq 0 \quad \text{(non-negativity constraints)} \end{aligned} \]

The maximum value of \(Z = 3x + 4y\) subject to the constraints \(x + y \leq 1\), \(x \geq 0\), \(y \geq 0\) is:
In an LPP, corner points of the feasible region determined by the system of linear constraints are \((1,1), (3,0), (0,3)\). If \(Z = ax + by\), where \(a>0, b>0\) is to be minimized, the condition on \(a\) and \(b\) so that the minimum of \(Z\) occurs at \((3, 0)\) and \((1, 1)\) will be: