Chapter 8Linear programming (I)8.1IntroductionDecision making is a process that has to be carried out in many areas of life. Usuallythere is a particular aim in making one decision rather than another. Two particular aimsthat are often considered in commerce are maximising profit and minimising loss.During, and after, the Second World War a group of American mathematicians developedsome mathematical methods to help with decision making. They sought to producemathematical models of situations in which all the requirements, constraints andobjectives were expressed as algebraic equations. They then developed methods forobtaining the optimal solution – the maximum or minimum value of a requiredfunction.In this chapter we will study problems for which all the algebraic expressions are linear,that is, of the form(a number)x + (a number)y;For example,Profit=4x + 3yis a linear equation in x and y, and16x + 18y ≤ 25is a linear inequation or inequality in x and y. This area of mathematics is called linearprogramming.Linear programming methods are some of the most widely used method employed tosolve management and economic problems. They have been applied in a variety ofcontexts, some of which will be discussed in this chapter, with enormous savings inmoney and resources.71
CHAPTER 8. LINEAR PROGRAMMING (I)728.2Formulating linear programming problems.