Evaluate \(\int_{c}(\bar{Z}+2z)dz\) along the circle c: \( x^{2}+y^{2}=1\)

Find dual of following LP model

max z= 2x_{1} +3x_{2}+5x_{3}

Subjected to

x_{1}+x_{2}-x_{3}\(\ge\) -5

x_{1}+x_{2}+4x_{3}=10

-6x_{1}+7x_{2}-9x_{3}\(\le\)4

x_{1},x_{2}\(\ge\)0 and x_{3} is unrestricted.

Using Cauchy's integral formula,evaluate \(\int_{c} \dfrac{(12z-7)dz}{(z-1)^{2}(2z+3)}\)where C: |z+i|=\(\sqrt{3}\\\)

Determine whether matrix a is derogatory A =\(\begin{bmatrix} 2 &1 &0 \\ 0&2 &1 \\ 0&0 &2 \end{bmatrix}\\\)

The daily consumption of electric power (in millions of kwh)is r.v with PDF f(x) =k xe^{-x/30} ,x>0.find k and the probability that on a given day the electricity consumption is more than expected electricity consumption.

Using Simplex method, solve the following LPP

max z = 15x_{1}+6x_{2}+ 9x_{3}+2x_{4}

s.t2x_{1}+x_{2}+5x_{3}+6x_{4} \(\le\) 20

3x_{1} +x_{2}+3x_{3}+25x_{4}\(\le\)24

7x_{1}+x_{4}\(\le\)70

& x_{1},x_{2},x_{3},x_{4}\(\ge\) 0

Obtain ALL Taylor's and Laurent series expansion of function \(\dfrac{(z-1)(z+2)}{(z+1)(z+4)}about z=0\)

Age of car(in years):x | 2 | 4 | 6 | 8 |

maintenance cost :y (in thousands) | 5 | 7 | 8.5 | 11 |

Show that the matrix A is diagonalizable, Find its diagonal form and transforming matrix, if A =\(\begin{bmatrix} -9 &4 &4 \\ -8& 3 &4 \\ -16&8 &7 \end{bmatrix}\\\)

Using Dual simplex method,solve

max z = -2x_{1} -x_{3}

s.t x_{1} +x_{2} -x_{3} \(\ge
\)5

x_{1} -2x_{2} +4x_{3} \(\ge\)8

& x_{1} ,x_{2} ,x_{3} \(\ge\) 0

Maximize Z=2x

_{1 }

^{2}

_{ }

^{ }+12x

_{1}x

_{2}-7x

_{1}

^{2}

subject to the constraints 2x

_{1}+5x

_{2}≤ 98 and x

_{1}, x

_{2}7 ≥ 0