HSC Science (Electronics) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

The corner points of the feasible solution given by the inequation x + y ≤ 4, 2x + y ≤ 7, x ≥ 0, y ≥ 0 are ______.

The corner points of the feasible solution are (0, 0), (2, 0), `(12/7, 3/7)`, (0, 1). Then z = 7x + y is maximum at ______.

If the corner points of the feasible solution are (0, 0), (3, 0), (2, 1), `(0, 7/3)` the maximum value of z = 4x + 5y is ______.

If the corner points of the feasible solution are (0, 10), (2, 2) and (4, 0), then the point of minimum z = 3x + 2y is ______.

The half-plane represented by 3x + 2y < 8 contains the point ______.

The half-plane represented by 4x + 3y >14 contains the point ______.

Solve the following LPP:

Maximize z = 5x₁ + 6x₂ subject to 2x₁ + 3x₂ ≤ 18, 2x₁ + x₂ ≤ 12, x₁ ≥ 0, x₂ ≥ 0.

Solve the following LPP:

Maximize z = 4x + 2y subject to 3x + y ≤ 27, x + y ≤ 21, x ≥ 0, y ≥ 0.

Solve the following LPP:

Maximize z = 6x + 10y subject to 3x + 5y ≤ 10, 5x + 3y ≤ 15, x ≥ 0, y ≥ 0.

Solve the following LPP:

Maximize z = 2x + 3y subject to x - y ≥ 3, x ≥ 0, y ≥ 0.

Solve each of the following inequations graphically using XY-plane:

4x - 18 ≥ 0

Solve each of the following inequations graphically using XY-plane:

- 11x - 55 ≤ 0

Solve each of the following inequations graphically using XY-plane:

5y - 12 ≥ 0

Solve each of the following inequations graphically using XY-plane:

y ≤ - 3.5

Sketch the graph of the following inequation in XOY co-ordinate system:

|x + 5| ≤ y

Find graphical solution for the following system of linear in equation:

3x + 4y ≤ 12, x - 2y ≥ 2, y ≥ - 1

Solve the following LPP:

Maximize z = 4x₁ + 3x₂ subject to
3x₁ + x₂ ≤ 15, 3x₁ + 4x₂ ≤ 24, x₁ ≥ 0, x₂ ≥ 0. 

Solve the following LPP:

Maximize z =60x + 50y  subject to

x + 2y ≤ 40, 3x + 2y ≤ 60, x ≥ 0, y ≥ 0.

Solve the following LPP:

Minimize z = 4x + 2y

Subject to 3x + y ≥ 27, x + y ≥ 21, x + 2y ≥ 30, x ≥ 0, y ≥ 0

A carpenter makes chairs and tables. Profits are ₹ 140 per chair and ₹ 210 per table. Both products are processed on three machines: Assembling, Finishing and Polishing. The time required for each product in hours and availability of each machine is given by the following table:

Formulate the above problem as LPP. Solve it graphically