HSC Commerce इयत्ता १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Compute the consumer price index for 2015 on the basis of 2014 from the following data.

An Enquiry was made into the budgets of the middle class families in a city gave the following information.

What changes in the cost of living have taken place in the middle class families of a city?

What is the Assignment problem?

Give mathematical form of Assignment problem

What is the difference between Assignment Problem and Transportation Problem?

Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.

(cost is in ₹ per unit)

A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

Assign the programmers to the programme in such a way that the total computer time is least.

A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the time each man would take to perform each task is given below:

How should the tasks be allocated to subordinates so as to minimize the total manhours?

Find the optimal solution for the assignment problem with the following cost matrix.

Assign four trucks 1, 2, 3 and 4 to vacant spaces A, B, C, D, E and F so that distance travelled is minimized. The matrix below shows the distance.

Choose the correct alternative:

Number of basic allocation in any row or column in an assignment problem can be

Choose the correct alternative:

North – West Corner refers to ______

Choose the correct alternative:

If number of sources is not equal to number of destinations, the assignment problem is called ______

Choose the correct alternative:

The purpose of a dummy row or column in an assignment problem is to

Choose the correct alternative:

The solution for an assignment problem is optimal if

Choose the correct alternative:

In an assignment problem involving four workers and three jobs, total number of assignments possible are

A car hire company has one car at each of five depots a, b, c, d and e. A customer in each of the fine towers A, B, C, D and E requires a car. The distance (in miles) between the depots (origins) and the towers(destinations) where the customers are given in the following distance matrix.

How should the cars be assigned to the customers so as to minimize the distance travelled?

A natural truck-rental service has a surplus of one truck in each of the cities 1, 2, 3, 4, 5 and 6 and a deficit of one truck in each of the cities 7, 8, 9, 10, 11 and 12. The distance(in kilometers) between the cities with a surplus and the cities with a deficit are displayed below:

How should the truck be dispersed so as to minimize the total distance travelled?

The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine. Some of the people receiving this letter already subscribe to the magazine while others do not. From this mailing list, 45% of those who already subscribe will subscribe again while 30% of those who do not now subscribe will subscribe. On the last letter, it was found that 40% of those receiving it ordered a subscription. What percent of those receiving the current letter can be expected to order a subscription?

A new transit system has just gone into operation in Chennai. Of those who use the transit system this year, 30% will switch over to using metro train next year and 70% will continue to use the transit system. Of those who use metro train this year, 70% will continue to use metro train next year and 30% will switch over to the transit system. Suppose the population of Chennai city remains constant and that 60% of the commuters use the transit system and 40% of the commuters use metro train next year.

What percent of commuters will be using the transit system year after the next year?