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12th Business Maths Monthly Test - 2 ( Operations Research )

MABS Institution

12th Business Maths Monthly Test - 2 ( Operations Research )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

What is the Assignment problem?

Determine basic feasible solution to the following transportation problem using North west Corner rule.

Determine an initial basic feasible solution to the following transportation problem by using (i)North West Corner rule (ii) least cost method.

Obtain an initial basic feasible solution to the following transportation problem by using least- cost method.

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?

Obtain an initial basic feasible solution to the following transportation problem by north west corner method.

A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing season. The farmer has categorized the amount of rainfall as high medium and low. His estimated profit for each is shown in the table.

Rainfall Estimated Conditional Profit(Rs.)

crop A crop B crop C

High 8000 3500 5000

Medium 4500 4500 5000

Low 2000 5000 4000

If the farmer wishes to plant only crop, decide which should be his best crop using
(i) Maximin (ii)Minimax

What is the difference between Assignment Problem and Transportation Problem?

Explain Vogel’s approximation method by obtaining initial basic feasible solution of the following transportation problem.

Find the initial basic feasible solution of the following transportation problem:

Using (i) North West Corner rule
(ii) Least Cost method
(iii) Vogel’s approximation method

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.

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.

The following table summarizes the supply, demand and cost information for four factors S₁, S₂, S₃, S₄. shipping goods to three warehouses D₁, D₂, D₃.

Find an initial solution by using north west corner rule. What is the total cost for this solution?
Find an initial solution by using north west corner rule. What is the total cost for this solution?

What do you mean by balanced transportation problem?

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

Given the following pay-off matrix(in rupees) for three strategies and two states of nature.

Strategy States-of-nature

E₁ E₂

S₁ 40 60

S₂ 10 -20

S₃ -40 150

Select a strategy using each of the following rule (i) Maximin (ii) Minimax

Explain Vogel’s approximation method by obtaining initial feasible solution of the following transportation problem

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 man-hours?

A person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay-off matrix based on three potential economic conditions is given in the following table:

Alternative Economic conditions

High growth(Rs.) Normal growth(Rs.) Slow growth (Rs.)s

Stocks 10000 7000 3000

Bonds 8000 6000 1000

Debentures 6000 6000 6000

Determine the best investment plan using each of following criteria i) Maxmin ii) Minimax.

Find an initial basic feasible solution of the following problem using north west corner rule.

Write mathematical form of transportation problem.

What is transportation problem?

Consider the following transportation problem

Determine initial basic feasible solution by VAM

Give mathematical form of assignment problem.

The research department of Hindustan Ltd. has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-offs for various level of sales.

Types of shampoo Estimated Sales (in Units)

15000 10000 5000

Egg shampoo 30 10 10

Clinic Shampoo 40 15 5

Deluxe Shampoo 55 20 3

What will be the marketing manager’s decision if
(i) Maximin and
(ii) Minimax principle applied?

Determine an initial basic feasible solution of the following transportation problem by north west corner method

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?

Consider the following transportation problem

Determine an initial basic feasible solution using (a) Least cost method (b) Vogel’s approximation method.

Following pay-off matrix, which is the optimal decision under each of the following rule
(i) maxmin
(ii) minimax

Act States of nature

S₁ S₂ S₃ S₄

A₁ 14 9 10 5

A₂ 11 10 8 7

A₃ 9 10 10 11

A₄ 8 10 11 13

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 Rs. per unit)

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