代写MTH5114 Linear Programming and Game Theory, Spring 2024 Week 4 Coursework Questions调试SPSS

MTH5114 Linear Programming and Game Theory, Spring 2024

Week 4 Coursework Questions

These exercises should be completed individually and submitted (together with those of weeks 5 and 6) via the course QMPlus page by 9am on Monday, 11 March.

Make sure you clearly write your name and student ID number at the top of your submission. Note that the credit available for each week’s coursework exercises is roughly equal.

1. Suppose we have a linear program in standard equation form.

and suppose u, v. and w are all optimal solutions to this linear program.

(a) Prove that  is a feasible solution.

(b) Prove that  is an optimal solution.

(c) Your proofs for (b) and (c) should work more generally for certain linear com-binations of u, v, and w. State for which linear combinations of u, v, and w your proofs still work. (You do not have to justify your answer for part (c)).

Hint: for this question it is helpful to look at certain parts of the proofs covered in week 4 and to adapt them.