This article provides Answers for NPTEL Data Science for Engineers Assignment 5 Answers. If you haven't completed the Week 4 Assignment, the link is below. The answers provided here are 100% Correct. Most of them are revised from previous assignments. 

Also Read: NPTEL Data Science for Engineers Week 4 Assignment 2025

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NPTEL Data Science for Engineers Week 5 Assignment 2025

In this week 5, the following topics are discussed:

• Multivariate Optimization with Equality Constraints
• Multivariate Optimization with Inequality Constraints
• Solving Data Science Problems
• Dataset

Last Date: 26-02-2025

Q1. The values of μ1, μ2 and μ3 while evaluating the Karush-Kuhn-Tucker (KKT) condition with all the constraints being inactive are

A. μ1=μ2=μ3=1
B. μ1=μ2=μ3=0
C. μ1=μ3=0,μ2=1
D. μ1=μ2=0,μ3=1

Answer: [ B ]   μ1=μ2=μ3=0

Q2. Gradient based algorithm methods compute

A. only step length at each iteration
B. both direction and step length at each iteration
C. only direction at each iteration
D. none of the above

Answer: [ B ] both direction and step length at each iteration

Q3. The point on the plane x+y−2z=6x+y−2z=6 that is closest to the origin is

A. (0, 0, 0)
B. (1, 1, 1)
C. (−1, 1, 2)
D. (1, 1, −2)

Answer: [ D ] (1, 1, -2)

Q4. Find the maximum value of f(x,y)=49−x2−y2f(x,y)=49−x2−y2 subject to the constraints x+3y=10x+3y=10.

A. 49
B. 46
C. 59
D. 39

Answer: [ D ] 39 

Q5. The minimum value of f(x,y)=x2+4y2−2x+8yf(x,y)=x2+4y2−2x+8y subject to the constraint x+2y=7x+2y=7 occurs at the below point:

A. (5, 5)
B. (−5, 5)
C. (1, 5)
D. (5, 1)

Answer: [ D ] (5, 1)

Q6. Which of the following statements is/are NOT TRUE with respect to the multi variate optimization?

I - The gradient of a function at a point is parallel to the contours
II - Gradient points in the direction of greatest increase of the function
III - Negative gradients points in the direction of the greatest decrease of the function
IV - Hessian is a non-symmetric matrix

A. I
B. II and III
C. I and IV
D. III and IV

Answer:[ C ] I and IV

Q7. The solution to an unconstrained optimization problem is always the same as the solution to the constrained one.

A. True
B. False

Answer: [ B ] False

Q8. A manufacturer incurs a monthly fixed cost of $7350 and a variable cost,  C(m)=0.001m^3−2m^2+324m dollars. The revenue generated by selling these units is, R(m)=−6m^2+1065m. How many units produced every month (m)(m) will generate maximum profit?

A. m=46

B. m=90
C. m=231
D. m=125

Answer: [ B ] m = 90

Q9. Consider an optimization problem minx1,x^2−xy+y^2 subject to the constraints
2x+y≤12x+y≤1
x+2y≥2x+2y≥2
x≥−1x≥−1
Find the lagrangian function for the above optimization problem.

Answer: [ A ] 

Also Read: NPTEL Data Science for Engineers Week 4 Assignment 2025

Conclusion

Also Read: NPTEL Data Science for Engineers Week 6 Assignment 2025 Answers

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