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

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.

Choose the correct alternative :

The assignment problem is said to be balanced if it is a ______.

Solve the following problem :

Five jobs must pass through a lathe and a surface grinder, in that order. The processing times in hours are shown below. Determine the optimal sequence of the jobs. Also find the idle time of each machine.

Solve the following problem :

Find the sequence that minimizes the total elapsed time to complete the following jobs. Each job is processed in order AB.

Determine the sequence for the jobs so as to minimize the processing time. Find the total elapsed time and the idle times for both the machines.

Choose the correct alternative:

If there are 3 machines A, B and C, conditions for reducing a 3 machine problem to a 2 machine problem with respect to minimum processing time is ______

If there are n jobs and m machines, then there will be _______ sequence of doing jobs.

An unbalanced assignment problems can be balanced by adding dummy rows or columns with ______ cost

In sequencing problem the time which required to complete all the jobs i.e. entire task is called ______

The optimum sequence for the above data is ______

State whether the following statement is True or False:

In sequencing problem the processing times are dependent of order of processing the jobs on machine

Find the assignments of salesman to various district which will yield maximum profit

Find the sequence that minimizes total elapsed time to complete the following jobs in the order XY. Find the total elasped time and idle times for each machine.

For the following assignment problem minimize total man hours:

Subtract the `square` element of each `square` from every element of that `square`

Subtract the smallest element in each column from `square` of that column.

The lines covering all zeros is `square` to the order of matrix `square`

The assignment is made as follows:

Optimum solution is shown as follows:

A → `square, square` → III, C → `square, square` → IV

Minimum hours required is `square` hours

State whether the following statement is true or false:

To convert a maximization-type assignment problem into a minimization problem, the smallest element in the matrix is deducted from all elements of the matrix.