Which of the following is the correct dual of ?Question 13Answera.b.pc.qd.

Consider the statement given below and state its dual.Weather is cloudy and it is raining.Question 1Answera.It is not raining, and weather is not cloudy.b.Weather is cloudy, or it is not raining.c.Weather is not cloudy, and it is raining.d.It is raining, or weather is cloudy.

A primal linear program has the form:minx∈Rnc⊺xsubject toAx≥bmin𝑥∈𝑅𝑛𝑐⊺𝑥subject to𝐴𝑥≥𝑏where A𝐴 is an m×n𝑚×𝑛 matrix. The dual linear program has the form:maxy∈Rmb⊺ysubject to{Dy=cy≥0max𝑦∈𝑅𝑚𝑏⊺𝑦subject to{𝐷𝑦=𝑐𝑦≥0Which of the following is a correct expression for the matrix D𝐷?Question 3Answera.D=I𝐷=𝐼b.D=A⊺𝐷=𝐴⊺c.D=A𝐷=𝐴d.D=A+bc⊺

For a primal-dual pair of linear programs (where the primal is a minimisation problem and the dual is a maximisation problem), you are told that the optimal value of the dual linear program is 22. Which of the following statements is true?Question 1Answera.The primal linear program is infeasible.b.Any feasible point of the dual linear program has value at least 22.c.The primal linear program is unbounded.d.Any feasible point of the primal linear program has objective value of at least 22.

Consider the quadratic program minx1,x2f(x1,x2)subject toCx≥dmin𝑥1,𝑥2𝑓(𝑥1,𝑥2)subject to𝐶𝑥≥𝑑where C𝐶 is a 5×25×2 matrix and d𝑑 is a length 5 vector. (c) How many variables does the dual quadratic program have? Answer 4 Question 1(d) What is the value of the dual quadratic program at the point y=0𝑦=0?

Write the dual of the following linear programming problem:Maximize 8x1 + 3x2 − 2x3subject to x1 − 6x2 + x3 > 25x1 + 7x2 − 2x3 = −4x1 ≤ 0, x2 ≥ 0, x3 unrestricted.