## MAT A33 – Week 1

Posted in 2016 -- MATA33, Lecture Notes by pgadey on 2015/12/17

This blog post contains my notes for MAT A33. It includes links to my lecture notes, practice problems, and some additional references for the curious.

My lectures notes for this week are available here. A compressed PDF file of the lecture notes is available here.

Overview:

• Introduction to MATA33: course policies and overview
• Linear inequalities in two variables
• Linear programming terminology and method

Practice problems:

Exercise 1 (Exam Summer 2009) Find the maximum and minimum values of the function ${Z = -4x - 6y}$ subject to the contraints: ${y \geq 1}$, ${1 \leq x \leq 6}$, ${y \leq 2x + 1}$, and ${2x + 3y \leq 27}$.

Exercise 2 (Exam Winter 2013) If ${R}$ is the feasible region defined by the inequality ${0 \leq \frac{1 }{2 }x \leq y \leq x + 1}$ then for what values of the constant ${\alpha}$ does the function ${Z = \alpha x + y}$ not have maximum on value on ${R}$?