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BA · Data envelopment analysis (DEA)

25 questions · 38.5 marks · 4 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Business Analytics

Data envelopment analysis (DEA)

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

End Term · 31 Aug 2025 (FN)End Term

Read the passage below, then answer Q1–Q2
There are six business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 3, and you find that the efficiency is 0.9. You see that the dual variables corresponding to the constraints of business units 2 and 5 are non- zero, and the dual variables corresponding to the constraints of other units are zero. The dual variables corresponding to the constraints of business units 2 and 5 are 0.55 and 0.35, respectively. Based on Table 4, answers the given subquestions.
Hint: At every step, round off your answers to 4 decimal places.
Q1NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 1 in HCU 3? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 1000.63545, then enter the answer as “1000.6355”]
Your answer:
Q2NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 2 in HCU 3? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 1000.63545, then enter the answer as “1000.6355”]
Your answer:
Read the passage below, then answer Q3–Q5
We are interested in understanding the efficiency of 5 Sales Offices. Each of the Sales Offices has an approved budget and a team size for achieving a fixed target of 10,00,000. As a Business Analyst, you must formulate a DEA problem using Linear programming for the Sales Office 2. Answer the given subquestions using the Table below.
Q3MCQ1.5 Marks·Choose one option
Asked 3 times Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E
Q4MCQ1.5 Marks·Choose one option
Asked 3 times Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D
Q5MSQ1.5 Marks·Choose all correct options
Asked 3 times Key ↓
Which of them is not a constraint for the LP problem pertaining to Sales Office 2? (Select all that apply)
1. A
2. B
3. C
4. D
5. E
6. F

End Term · 31 Aug 2025 (AN)End Term

Read the passage below, then answer Q6–Q7
There are six business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 3, and you find that the efficiency is 0.8. You see that the dual variables corresponding to the constraints of business units 2 and 5 are non- zero, and the dual variables corresponding to the constraints of other units are zero. The dual variables corresponding to the constraints of business units 2 and 5 are 0.55 and 0.25, respectively. Based on Table 4, answers the given subquestions.
Hint: At every step, round off your answers to 4 decimal places.
Q6NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 1 in HCU 3? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 1000.63545, then enter the answer as “1000.6355”]
Your answer:
Q7NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 2 in HCU 3? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 1000.63545, then enter the answer as “1000.6355”]
Your answer:
Read the passage below, then answer Q8–Q10
We are interested in understanding the efficiency of 5 Sales Offices. Each of the Sales Offices has an approved budget and a team size for achieving a fixed target of 10,00,000. As a Business Analyst, you must formulate a DEA problem using Linear programming for the Sales Office 3. Answer the given subquestions using the Table below.
Q8MCQ2 Marks·Choose one option
Asked 3 times Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E
Q9MCQ2 Marks·Choose one option
Asked 3 times Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D
Q10MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Which of them is not a constraint for the LP problem pertaining to Sales Office 3?
1. A
2. B
3. C
4. D
5. E
6. F

End Term · 13 Apr 2025 (FN)End Term

Q11MSQ2 Marks·Choose all correct options
Key ↓
There are 7 business units and you are using the DEA to compare them. You solve the LP for business unit 5. You find from the constraint expression that business unit 1 has obtained an efficiency of 1 and business unit 2 has obtained an efficiency of 1 with the optimal weights of business unit 5. Which of the following statements is correct? (choose all that is/are applicable)
1. ABusiness unit 5 is inefficient
2. BBusiness unit 1 is efficient
3. CBusiness unit 5 is efficient
4. DBusiness unit 2 is efficient
Q12MSQ2 Marks·Choose all correct options
Key ↓
In DEA, when can the Linear Programming model be used for calculating the weights of efficiency (weighted outputs/weighted inputs)? (choose all that is/are applicable)
1. AAfter converting the ratio into the linear objective function
2. BAfter normalizing the denominator
3. CBy setting a constraint on the efficiency of all DMUs to be lesser than or equal to 1
4. DNone of these
Read the passage below, then answer Q13–Q14
There are six business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 3, and you find that the efficiency is 0.8. You see that the dual variables corresponding to the constraints of business units 2 and 5 are non- zero, and the dual variables corresponding to the constraints of other units are zero. The dual variables corresponding to the constraints of business units 2 and 5 are 0.5 and 0.3, respectively. Based on Table 6, answers the given sub-questions
Q13NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 1 in HCU 3?
Your answer:
Q14NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 2 in HCU 3?
Your answer:
Read the passage below, then answer Q15–Q17
As a Business Analyst, we are trying to find the DMUs that are efficient, where there are 2 outputs (Number of Leads & Sales) and one constant input. Based on the graph given in Figure-4 below, answer the given sub-questions
Q15MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Which DMUs are in the economic frontier?
1. A(3,2,1)
2. B(3,2,5)
3. C(4,5,2)
4. D(3,4,1)
Q16MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Which DMUs are the reference units for DMU 2?
1. A(5,4)
2. B(4,1)
3. C(3,5)
4. D(3,1)
Q17MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Which DMUs are the reference units for DMU 5?
1. A(1,4)
2. B(1,3)
3. C(3,4)
4. DNone of these

End Term · 22 Dec 2024 (AN)End Term

Read the passage below, then answer Q18–Q20
We are interested in understanding the efficiency of 5 Sales Offices. Each of the Sales Offices has an approved budget and a team size for achieving a fixed target of 20,00,000. As a Business Analyst, you must formulate a DEA problem using Linear programming for the Sales Office 3. Answer subquestions using the Table below.
Q18MCQ1 Mark·Choose one option
Asked 3 times Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E
Q19MCQ1 Mark·Choose one option
Asked 3 times Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D
Q20MCQ1 Mark·Choose one option
Asked 3 times Key ↓
Which of them is not a constraint for the LP problem pertaining to Sales Office 3?
1. A
2. B
3. C
4. D
5. E
6. F
Read the passage below, then answer Q21–Q22
There are 5 business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 3 and find that the efficiency to be 0.6. You find that the dual variables corresponding to the constraints of business units 2 and 4 are non-zero and the dual variables corresponding to the constraints of other units are zero. The dual variables corresponding to the constraints of business units 2 and 4 are 0.25 and 0.35, respectively. You are given the following table where sales and number of leads are the two outputs.
Based on the above data, answer the given subquestions.
Q21NAT1.5 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 1 in HCU 3? NOTE: For every step performed round off 4 decimal places.
Your answer:
Q22NAT1.5 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 2 in HCU 3? NOTE: For every step performed round off 4 decimal places.
Your answer:
Read the passage below, then answer Q23–Q25
As a Business Analyst, we are trying to find the DMUs that are efficient, where there are 2 inputs (Team Size & Budget) and one constant output. Based on the graph given below, answer the subquestions
Q23MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Which DMUs are in the economic frontier?
1. A(1,2,4)
2. B(1,3,5)
3. C(1,2,4,5)
4. D(1,3,4)
Q24MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Which DMUs are the reference units for DMU 2?
1. A(1,4)
2. B(1,3)
3. C(3,5)
4. D(3,4)
Q25MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Which DMUs are the reference units for DMU 4?
1. A(1,4)
2. B(1,3)
3. C(3,5)
4. D(3,4)

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q16915 to 6918

Q227.5 to 27.9

Q3C

Q4A

Q5F

Q67874 to 7876

Q717.1 to 17.3

Q8C

Q9A

Q10F

Q11B, D

Q12A, B, C

Q138061 to 8064

Q1410.5 to 11

Q15D

Q16B

Q17C

Q18C

Q19A

Q20F

Q217541 to 7542

Q2211.13 to 11.23

Q23B

Q24B

Q25C

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.