## NPTEL Data Science For Engineers Week 5 Assignment Answers 2024

1. The values of μ_{1}, μ_{2} and μ_{3} while evaluating the Karush-Kuhn-Tucker (KKT) condition with all the constraints being inactive are

- μ
_{1}=μ_{2}=μ_{3}=1 - μ
_{1}=μ_{2}=μ_{3}=0 - μ
_{1}=μ_{3}=0,μ_{2}=1 - μ
_{1}=μ_{2}=0,μ_{3}=1

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2. Gradient based algorithm methods compute

- only step length at each iteration
- both direction and step length at each iteration
- only direction at each iteration
- none of the above

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

- (0, 0, 0)
- (1, 1, 1)
- (−1, 1, 2)
- (1, 1, −2)

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4. Find the maximum value of f(x,y)=49−x^{2}−y^{2} subject to the constraints x+3y=10

- 49
- 46
- 59
- 39

Answer :-

5. The minimum value of f(x,y)=x^{2}+4y^{2}−2x+8y subject to the constraint x+2y=7 occurs at the below point:

- (5, 5)
- (−5, 5)
- (1, 5)
- (5, 1)

Answer :-

6. 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

- I
- II and III
- I and IV
- III and IV

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

- True
- False

Answer :-

8. 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) will generate maximum profit?

- m=46
- m=90
- m=231
- m=125

Answer :-

9.

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