HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

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The half plane represented by 3x + 2y ≤ 0 constraints the point.

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The half plane represented by 4x + 3y ≥ 14 contains the point

The optimal value of the objective function is attained at the ______ points of the feasible region.

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“A gorage employs eight men to work in its shownroom and repair shop. The constraints that there must be at least 3 men in showroom and at least 2 men in repair shop are ______ and _______ respectively.

A train carries at least twice as many first class passengers (y) as second class passengers (x). The constraint is given by ______.

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A dish washing machine holds up to 40 pieces of large crockery (x) This constraint is given by_______.

State whether the following is True or False :

Saina wants to invest at most ₹ 24000 in bonds and fixed deposits. Mathematically this constraints is written as x + y ≤ 24000 where x is investment in bond and y is in fixed deposits.

State whether the following is True or False :

The point (1, 2) is not a vertex of the feasible region bounded by 2x + 3y ≤ 6, 5x + 3y ≤ 15, x ≥ 0, y ≥ 0.

State whether the following is True or False :

The feasible solution of LPP belongs to only quadrant I.

The Cost of Living Index Number using Weighted Relative Method is given by ______

The Assignment Problem is solved by ______.

To use the Hungarian method, a profit maximization assignment problem requires ______.

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Using Hungarian method the optimal assignment obtained for the following assignment problem to minimize the total cost is:

Fill in the blank :

For solving an assignment problem the matrix should be a _______ matrix.

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In Hungarian Method, only _______ task can be assigned to each facility.

State whether the following is True or False :

The Hungarian method operates on the principle of matrix reduction, whereby the cost table is reduced to a set of opportunity costs.

State whether the following is True or False :

Optimal assignments are made in the Hungarian method to cells in the reduced matrix that contain a zero.

State whether the following is True or False :

Using the Hungarian method, the optimal solution to an assignment problem is found when the minimum number of lines required to cover the zero cells in the reduced matrix equals the no of persons.

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers. Find E(X).