# Optimization Techniques Unit-4 Quiz

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• 1.

### Identify 3 IBFS methods of a transportation problem

• A.

MODI method

• B.

North-West Corner Method

• C.

Least Cost  Method

• D.

Vogel's Approximation  Method

B. North-West Corner Method
C. Least Cost  Method
D. Vogel's Approximation  Method
Explanation
The three IBFS (Initial Basic Feasible Solution) methods of a transportation problem are the North-West Corner Method, the Least Cost Method, and Vogel's Approximation Method. The North-West Corner Method starts by allocating units from the top-left corner of the transportation table and gradually moves towards the bottom-right corner. The Least Cost Method selects the cell with the lowest cost to allocate units and repeats this process until all cells are filled. Vogel's Approximation Method considers the difference between the two lowest costs in each row and column to determine the best allocation.

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• 2.

### Identify BFS method of a transportation problem

• A.

North-West Corner Method

• B.

Least Cost Method

• C.

Vogel's Approximation Method

• D.

MODI Method

D. MODI Method
Explanation
The MODI method is a method used in transportation problems to find an optimal solution. It stands for Modified Distribution Method. This method involves calculating the opportunity costs for each empty cell in the transportation table and selecting the cell with the highest opportunity cost. It then performs a cycle test to check if the solution is optimal. If the solution is not optimal, the method adjusts the allocation of units in the transportation table and repeats the process until an optimal solution is reached.

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• 3.

### Another name of the MODI(Modified Distribution) Method is u-v Method ?

• A.

True

• B.

False

A. True
Explanation
The statement is true because the MODI (Modified Distribution) Method is also known as the u-v Method. This method is used in linear programming to find the optimal solution of a transportation problem. It involves modifying the initial solution by evaluating the opportunity costs of reallocating units from one cell to another. Therefore, the alternative name for the MODI Method is u-v Method.

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• 4.

• A.

Option 1

• B.

Option 2

• C.

Option 3

• D.

Option 4

D. Option 4
• 5.

### Find the Total cost of below transportation problem using Least Cost Method

• A.

3000

• B.

2800

• C.

2900

• D.

3100

C. 2900
Explanation
Total Cost = (1*300)+(2*250)+(6*50)+(5*100)+(3*300)+(2*200)
= 300 + 500 + 300 + 500 + 900 + 400
∴ Total Cost = 2900

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• 6.

### Given Transportation Problem is

• A.

Unbalanced Transportation Problem

• B.

Balanced Transportation Problem

B. Balanced Transportation Problem
Explanation
Since given transportation problem is said to be balance means
Sum of all supply costs = Sum of all Demand costs
300 + 400 + 500 = 250 + 350 + 400 + 200
1200 = 1200

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• 7.

• A.

Option 1

• B.

Option 2

• C.

Option 3

• D.

Option 4

C. Option 3
• 8.

### Equation of No.of optimal cells of given transportation problem

• A.

M-n+1

• B.

M+n-2

• C.

M+n-1

• D.

M+n+1

C. M+n-1
Explanation
Here no. of rows, m = 3 and no. of columns , n = 4
No. of optimal cells = m + n – 1
= 3 + 4 – 1
∴ No. of optimal cells = 6

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• 9.

### The transportation problem is a special class of the linear programming problem

• A.

True

• B.

False

A. True
Explanation
The transportation problem is indeed a special class of the linear programming problem. It involves determining the optimal way to transport goods from sources to destinations, while minimizing the total cost or maximizing the total profit. It can be solved using various mathematical techniques, such as the simplex method or the transportation simplex method. Therefore, the statement is true.

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