HSC Commerce इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Draw the graph of the following function:

f(x) = e^2x

Draw the graph of the following function:

f(x) = e^-2x

Draw the graph of the following function:

f(x) = `|x|/x`

Solve the following linear programming problems by graphical method.

Maximize Z = 6x₁ + 8x₂ subject to constraints 30x₁ + 20x₂ ≤ 300; 5x₁ + 10x₂ ≤ 110; and x₁, x₂ ≥ 0.

Solve the following linear programming problems by graphical method.

Maximize Z = 22x₁ + 18x₂ subject to constraints 960x₁ + 640x₂ ≤ 15360; x₁ + x₂ ≤ 20 and x₁, x₂ ≥ 0.

Solve the following linear programming problems by graphical method.

Minimize Z = 3x₁ + 2x₂ subject to the constraints 5x₁ + x₂ ≥ 10; x₁ + x₂ ≥ 6; x₁ + 4x₂ ≥ 12 and x₁, x₂ ≥ 0.

Solve the following linear programming problems by graphical method.

Maximize Z = 40x₁ + 50x₂ subject to constraints 3x₁ + x₂ ≤ 9; x₁ + 2x₂ ≤ 8 and x₁, x₂ ≥ 0.

Solve the following linear programming problems by graphical method.

Maximize Z = 20x₁ + 30x₂ subject to constraints 3x₁ + 3x₂ ≤ 36; 5x₁ + 2x₂ ≤ 50; 2x₁ + 6x₂ ≤ 60 and x₁, x₂ ≥ 0.

Solve the following linear programming problems by graphical method.

Minimize Z = 20x₁ + 40x₂ subject to the constraints 36x₁ + 6x₂ ≥ 108; 3x₁ + 12x₂ ≥ 36; 20x₁ + 10x₂ ≥ 100 and x₁, x₂ ≥ 0.

Maximize: z = 3x₁ + 4x₂ subject to 2x₁ + x₂ ≤ 40, 2x₁ + 5x₂ ≤ 180, x₁, x₂ ≥ 0. In the LPP, which one of the following is feasible comer point?

A solution which maximizes or minimizes the given LPP is called

In the given graph the coordinates of M₁ are

The maximum value of the objective function Z = 3x + 5y subject to the constraints x ≥ 0, y ≥ 0 and 2x + 5y ≤ 10 is:

The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤ 20, x + 2y ≤ 20, x > 0 and y > 0 is

Given an L.P.P maximize Z = 2x₁ + 3x₂ subject to the constrains x₁ + x₂ ≤ 1, 5x₁ + 5x₂ ≥ 0 and x₁ ≥ 0, x₂ ≥ 0 using graphical method, we observe

A firm manufactures two products A and B on which the profits earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M₁ and M₂. Product A requires one minute of processing time on M₁ and two minutes on M₂, While B requires one minute on M₁ and one minute on M₂. Machine M₁ is available for not more than 7 hrs 30 minutes while M₂ is available for 10 hrs during any working day. Formulate this problem as a linear programming problem to maximize the profit.

A firm manufactures pills in two sizes A and B. Size A contains 2 mgs of aspirin, 5 mgs of bicarbonate and 1 mg of codeine. Size B contains 1 mg. of aspirin, 8 mgs. of bicarbonate and 6 mgs. of codeine. It is found by users that it requires at least 12 mgs. of aspirin, 74 mgs. of bicarbonate and 24 mgs. of codeine for providing immediate relief. It is required to determine the least number of pills a patient should take to get immediate relief. Formulate the problem as a standard LLP.

Solve the following linear programming problem graphically.

Maximise Z = 4x₁ + x₂ subject to the constraints x₁ + x₂ ≤ 50; 3x₁ + x₂ ≤ 90 and x₁ ≥ 0, x₂ ≥ 0.

Solve the following linear programming problem graphically.

Minimize Z = 200x₁ + 500x₂ subject to the constraints: x₁ + 2x₂ ≥ 10; 3x₁ + 4x₂ ≤ 24 and x₁ ≥ 0, x₂ ≥ 0.

Solve the following linear programming problem graphically.

Maximize Z = 3x₁ + 5x₂ subject to the constraints: x₁ + x₂ ≤ 6, x₁ ≤ 4; x₂ ≤ 5, and x₁, x₂ ≥ 0.