MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 14Question 1:Compute The Principal Minors, The Hessian, And The Bordered Hessian Of The Following Func Tions:(A) F(X, Y, Z) = Ex+Y + Z.(B) G(X, Y) = Xy.(C) H(X, Y) = Excos Y.Question 2:Consider The Functiondefined For X, Y &>
分类：
编程语言 时间：
2025/2/17 10:47:29
MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 13Question 1:For Which A ∈ R Is The Function F ∶ R3 ! R, F(X, Y, Z) = X2 + Xz + Ayz + Z2convex?Question 2:Show That The Function F ∶ R4 ! R, With F(X, Y, Z, W) = X2 + Y2 + Z2 + W2 − 2Xw − 4Yz Is Neither Convex Nor Concave On R4
分类：
编程语言 时间：
2025/1/26 19:34:42
MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 12Question 1:Determine Whether Each Of The Following Is True Or False. Justify Your Answers.(1) If S1 And S2 Are Two Convex Sets In R2, Then Their Unions1 ∪ S2 = {X ∈ R2∶ X ∈ S1 Or X ∈ S2}Must Be A Convex Set In R2.(2) If F And
分类：
编程语言 时间：
2025/1/25 10:55:53
MATH2003J,& & OPTIMIZATION& IN& & ECONOMICS,BDIC& & 2023/2024,& & Springproblem& Sheet& 11Θ& & Question& 1:Consider& The& Sets:A& =& {(X,& Y)& ∈& R2 & ∣ X2& +& Y2 & ≤& 4, ∣Y∣& ≤& 1}B& =& {(X,& 0)& ∈& R2 & ∣ X& ∈ [0, 10]}C& =&
分类：
编程语言 时间：
2025/1/23 14:53:20
MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 10Question 1:Let F ∶ R2 → R Be Defined By F(X, Y) = −20X − 10Y2and The Constraintsx2 + Y2≤ 100 And X ≥ 0.(I) Sketch The Feasible Set And Show That It Is Closed And Bounded. Conclude That F Achieves Both Its Maxima And Minima Un
分类：
编程语言 时间：
2025/1/22 12:33:37
MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 8Question 1:Consider The Following LP Problem:Maximize Z = 5X1+3X2subject To 2X1 + 4X2 ≤ 323X1 + 2X2 ≤ 24X1, X2 ≥ 0(I) Solve The Original Problem With The Simplex Method.(II) Formulate The Dual Problem.(III) Determine The Optim
分类：
编程语言 时间：
2025/1/16 12:55:53
MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 7Question 1:Formulate The Dual Problem Of The LP Problem:Maximize Z = −3X1 + 2X2subject To X1 − X2 ≤ 3,−X1 + X2 ≤ 6,X1, X2 ≥ 0.Question 2:Formulate The Dual Problem Of The LP Problem:Maximize Z = 16X1 + 25X2subject To X1 + 2X2
分类：
编程语言 时间：
2025/1/16 12:55:51
MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 6Question 1:Solve The Following LP Problem By The Simplex Method:Minimize Z = 3X1−2X2subject To X1 − X2 ≤ 1,X1 − X2 ≥ −2,X1, X2 ≥ 0.Question 2:Solve The Following LP Problem By The Simplex Method:Maximize Z = 8X1 + 2X2+2X3subje
分类：
编程语言 时间：
2025/1/15 11:25:54
MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 5Question 1:Consider The Following LP Problem:Maximize Z = 7X1 + 4X2subject To 2X1 + X2 ≤ 20,X1 + X2 ≤ 18,X1, X2 ≥ 0.(I) Solve The Above Problem Using The Graphical Method.(II) Solve The Above Problem Using The Simplex Method.Q
分类：
编程语言 时间：
2025/1/15 11:25:51
MATH2003J, OPTIMIZATION IN ECONOMICS,BDIC 2023/2024, Springproblem Sheet 4Question 1:In Each Of The Following, Transform. The Constraint Set Of The Linear Programming Problem Into The Standard Form, Incorporating All Supplemental Variables.(A).3X1 + X2 ≤ 25X1 + 5X2 ≤ 12X1, X2 ≥ 0.(B).X1 ≤ 22X2 ≤ 13X
分类：
编程语言 时间：
2025/1/13 18:30:20
1