NPTEL Data Science For Engineers Week 5 Assignment Answers 2024
1. The values of μ1, μ2 and μ3 while evaluating the Karush-Kuhn-Tucker (KKT) condition with all the constraints being inactive are
- μ1=μ2=μ3=1
- μ1=μ2=μ3=0
- μ1=μ3=0,μ2=1
- μ1=μ2=0,μ3=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−x2−y2 subject to the constraints x+3y=10
- 49
- 46
- 59
- 39
Answer :-
5. The minimum value of f(x,y)=x2+4y2−2x+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)=0.001m3−2m2+324m
dollars. The revenue generated by selling these units is, R(m)=−6m2+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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