HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

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 for each machine is given in the following table:

Find the optimal assignment to minimize the total processing cost.

Five wagons are available at stations 1, 2, 3, 4, and 5. These are required at 5 stations I, II, III, IV, and V. The mileage between various stations are given in the table below. How should the wagons be transported so as to minimize the mileage covered?

Five different machines can do any of the five required jobs, with different profits resulting from each assignment as shown below:

Find the optimal assignment schedule.

The assignment problem is said to be unbalance if ______

The assignment problem is said to be balanced if ______.

Choose the correct alternative :

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

Choose the correct alternative :

In an assignment problem if number of rows is greater than number of columns then

The objective of an assignment problem is to assign ______. 

Fill in the blank :

When an assignment problem has more than one solution, then it is _______ optimal solution.

Fill in the blank :

An _______ is a special type of linear programming problem.

In an assignment problem, if number of column is greater than number of rows, then a dummy column is added.

State whether the following is True or False :

In assignment problem, each facility is capable of performing each task.

State whether the following is True or False :

It is not necessary to express an assignment problem into n x n matrix.

Solve the following problem :

A plant manager has four subordinates, and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. This estimate of the time each man would take to perform each task is given in the effectiveness matrix below.

How should the tasks be allocated, one to a man, as to minimize the total man hours?

Solve the following problem :

A dairy plant has five milk tankers, I, II, III, IV and V. These milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.

How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?

If X has Poisson distribution with m = 1, then find P(X ≤ 1) given e⁻¹ = 0.3678

If X~P(0.5), then find P(X = 3) given e^−0.5 = 0.6065.

If X has Poisson distribution with parameter m and P(X = 2) = P(X = 3), then find P(X ≥ 2). Use e⁻³ = 0.0497

The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives only two complaints on a given day

The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives a) only two complaints on a given day, b) at most two complaints on a given day. Use e⁻⁴ = 0.0183.