Instructions:

Attempt all questions.

Each question has same marks.

Question $1$: Consider the following functions,

$($i$)f(x)=(x-5{)}^2$

$($ii$)f(x)=cos(x)+(x-3{)}^2$

Identify the

$($i$)$ local and glohal maxima in all the functions.

$($ii$)$ local and global minima in all the functions.

Question $2$: Convert the following linear programming problem to standard form:

max$(2x_1+x_2)$

$0x_{1}2$

$x_1+x_{2}3$

$x_1+2x_{2}5$

$x_{2}0$

Question $3$: What is Knapsack problem. Write it as an IP $($Integer Programming$)$ formulation

nd its LP $($Linear Programming$)$ relaxation.

Question $4$: Describe steps in the Particle Swarm Optimization $($PSO$)$ Algorithm.

Question $5$: Minimize the following function using the Lagrange multiplier method.

minf$(x,y)=5x^{-1}{y}^{-2}+37$