List of top Mathematics Questions on Linear Programming asked in UP Board XII

Minimize \(z=3x+2y\) under the following constraints by graphical method: \(x+y\ge8,\ x\ge0,\ 3x+5y\le15,\ y\ge0\).

Maximize \(Z=105x+90y\) under the constraints \(2x+y\le80,\ x+y\le50,\ x\ge0,\ y\ge0\) by graphical method.

Maximize \(Z=10x+3y\) by the graphical method under the following constraints: \(x\ge0;\ y\ge0;\ 5x+3y\le15;\ 2x+5y\le10\).

Find the minimum value of the linear programming problem \(Z=200x+500y\) under the following constraints: \(x+2y\ge10\), \(3x+4y\le24\), \(x\ge0,y\ge0\) by graphical method.

Find the minimum value of the objective function \(Z=3x+5y\) under the following constraints by the graphical method: \(x+3y\ge3,\ x+y\ge2,\ x\ge0,\ y\ge0\).

Find the maximum value of the objective function \(Z=5x+10y\) by graphical method under the following constraints: \(x+2y\le120\), \(x+y\ge60\), \(x-2y\ge0\), \(x\ge0\), \(y\ge0\).