运筹学代考 Operations Research代写

Midterm of ECEGY 6233 Spring 2021

运筹学代考 Determine the plastic moment capacities Mb , M c and the plastic hinge moments M 3 , M4, M5 for the above formulation.

Problem 1:  运筹学代考

Given f  =

4x2₂¹  + 3x2₂²  – 4x₁ x₂  + x₁ ,  the point X₀  = (-1/ 8,  0)^T  ,  and the direction vector d₀= – (1/ 5,  2 / 5)^T

(i) Is d₀ a decent direction?

(ii) Denoting g(a ) =  f (x₀  + ad₀ ),  find dg(1) / da ,  or equivalently, g’(1).

Problem 2: 运筹学代考

Consider a minimum weight design problem based on plastic collapse formulated by

minimize

P = 8M_b + 8M_c

subject to M₃ ≤Mb ,

M₄ ≤Mc ,

M₅≤ Mc ,

2M₃ – 2M₄ + M₅ -1120 ≤M_c,

2M₃ – M₄ – 800 ≤ M_b ,

2M₃ – M₄– 800 ≤M_c ,

M_b  ≥ 0, M_c  ≥ 0,

M₃  , M 4 , M 5 unrestricted in sign

Determine the plastic moment capacities Mb , M c and the plastic hinge moments M 3 , M₄, M₅ for the above formulation.

Problem 3:  运筹学代考

Consider the following constrained minimization problem

minimizef = 0.01x₂ + x₂

subject to

g₁= 25 –_x1x₂ ≤ 0,

g₁ = 2 – _x1 ≤ 0,

_x1 ≥0,x₂ ≥ 0

(i)Obtain the solution graphically.

(ii)Obtain the solution using KKT condition.

(iii)Verify the sufficient conditions for optimality.

 

更多代写：美国Matlab代写  天文学代考  台湾essay代写  土木工程essay代写  台湾论文代写  音乐Essay代写

合作平台：essay代写 论文代写 写手招聘 英国留学生代写