# NPTEL Data Science for Engineers Assignment 5 Answers 2022

## NPTEL Data Science for Engineers Assignment 5 Answers

Q1. An optimization problem, solved for N variables, with one equality constraint will have

a. N equations in N variables
b. N + 1 equations in N + 1 variables
c. N equations in N + 1 variables
d. none of these

Answer: b. N + 1 equations in N + 1 variables

Q2. While minimizing a function f(x,y)=6×2+4y2 with a constraint 3x+2y≤12, the unconstrained minimum solution is __________ the constrained minimum solution

a. Equal to

b. Less than

c. Greater than

d. both (b) and (c)

Q3. The function min f(x,y)=3x+y subject to the given constraints x2+y2<10 is an example of

a. Unconstrained multivariate optimisation

b. Multivariate optimisation with equality constraint

c. Multivariate optimisation with inequality constraint

d. None of the above

Answer: c. Multivariate optimisation with inequality constraint

Q4. What is the global minimum value for the function f(x,y)=(x+y)2+5?

a. 0

b. -∞

c. 5

d. global minimum does not exist

Consider the function f(x,y)=5x2+3y2;+8xy+12x+6y as the function to be optimized and answer questions 5 and 6.

Q5. The saddle point of the function f(x,y) exists in which of the following coordinates (x,y)

a. (6,-9)

b. (5,3)

c. (2,-3)

d. There is no saddle point

Q6. The Hessian matrix obtained for the function f(x,y) is

a.

\begin{bmatrix} 5 & 3 \\ 12 & 6 \end{bmatrix}

b.

\begin{bmatrix} 12 & 6 \\ 5 & 3 \end{bmatrix}

c.

\begin{bmatrix} 10 & 8 \\ 8 & 6 \end{bmatrix}

d.

\begin{bmatrix} 5 & 8 \\ 8 & 3 \end{bmatrix}

\begin{bmatrix} 10 & 8 \\ 8 & 6 \end{bmatrix}

Q7. The eigenvalues for the Hessian matrix obtained in Q6 are

a. -2.5, 2.5

b. 8.3584, -3.46

c. 4.5046, -5.3654

d. 16.2462, -0.2462

Q8. Geometrically, finding the minimum of the function f(x,y)=x2+4y2 subject to the constraint 3x+7y=4 implies that

a. The minimum value exist in the the gradient of the tangent 3x + 7y = 4

b. The minimum value is present in the contour of the ellipse x² + 4y² = k such that it’s tangent is 3x + 7y = 4

c. The minimum value is present at the point (0,0)

d. The minimum value is not dependent on the constraint

Answer: b. The minimum value is present in the contour of the ellipse x² + 4y² = k such that it’s tangent is 3x + 7y = 4

Q9. State whether the following statements are True or False.

i) The decision variables of the optimization function need not be independent of each other

ii) An optimization problem with linear objective function and linear constraints is said to be a linear optimization problem

a. i) – TRUE; ii) – FALSE

b. i) – FALSE; ii) – FALSE

c. i) – TRUE; ii) – TRUE

d. i) – FALSE; ii) – TRUE

Answer: d. i) – FALSE; ii) – TRUE

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