HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

Maximize Z = 60x + 50y Subject to x + 2y ≤ 40, 3x + 2y ≤ 60, x ≥ 0, y ≥ 0

Choose the correct alternative:

The feasible region is

Choose the correct alternative:

The point at which the minimum value of Z = 8x + 12y subject to the constraints 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0 is obtained at the point

Choose the correct alternative:

The corner points of feasible region for the inequations, x + y ≤ 5, x + 2y ≤ 6, x ≥ 0, y ≥ 0 are

State whether the following statement is True or False:

If the corner points of the feasible region are `(0, 7/3)`, (2, 1), (3, 0) and (0, 0), then the maximum value of Z = 4x + 5y is 12

A doctor prescribed 2 types of vitamin tablets, T₁ and T₂ for Mr. Dhawan. The tablet T₁ contains 400 units of vitamin and T₂ contains 250 units of vitamin. If his requirement of vitamin is at least 4000 units, then the inequation for his requirement will be ______

Heramb requires at most 400 calories from his breakfast. Every morning he likes to take oats and milk. If each bowl of oats and a glass of milk provides him 80 calories and 50 calories respectively, then as a constraint this information can be expressed as ______

Smita is a diet conscious house wife, wishes to ensure certain minimum intake of vitamins A, B and C for the family. The minimum daily needs of vitamins A, B, and C for the family are 30, 20, and 16 units respectively. For the supply of the minimum vitamin requirements Smita relies on 2 types of foods F₁ and F₂. F₁ provides 7, 5 and 2 units of A, B, C vitamins per 10 grams and F₂ provides 2, 4 and 8 units of A, B and C vitamins per 10 grams. F₁ costs ₹ 3 and F₂ costs ₹ 2 per 10 grams. How many grams of each F₁ and F₂ should buy every day to keep her food bill minimum

Minimize Z = 2x + 3y subject to constraints

x + y ≥ 6, 2x + y ≥ 7, x + 4y ≥ 8, x ≥ 0, y ≥ 0

Solve the following LPP graphically:

Maximize Z = 9x + 13y subject to constraints

2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0

Solution: Convert the constraints into equations and find the intercept made by each one of it.

The feasible region is OAPC, where O(0, 0), A(0, 6),

P( ___, ___ ), C(5, 0)

The optimal solution is in the following table:

∴ Z is maximum at __( ___, ___ ) with the value ___.

Solve the following LP.P.

Maximize z = 13x + 9y,

Subject to 3x + 2y ≤ 12,

x + y ≥ 4,

x ≥ 0,

y ≥ 0.

The set of feasible solutions of LPP is a ______.

Conditions under which the object function is to be maximum or minimum are called ______.

Shraddho wants to invest at most ₹ 25,000/- in saving certificates and fixed deposits. She wants to invest at least ₹ 10,000/- in saving certificate and at least ₹ 15,000/- in fixed deposits. The rate of interest on saving certificate is 5% and that on fixed deposits is 7% per annum. Formulate the above problem as LPP to determine maximum income yearly.

Solution which satisfy all constraints is called ______ solution.

Graphical solution set of the inequations x ≥ 0 and y ≤ 0 lies in ______ quadrant.

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job is given in the following table:

 How should the jobs be assigned to the four machines so that the total processing cost is minimum?

Solve the following minimal assignment problem and hence find the minimum value : 

Suggest optimum solution to the following assignment. Problem, also find the total minimum service time.
                                             Service Time ( in hrs.)

Solve the following minimal assignment problem :