TABLE OF CONTENTS This chapter is a continuation of Chapter 2. It is intended for readers who need the knowledge for more advanced topics in mathematics. It serves as a prerequisite for probability and statistics. Readers with a strong mathematical background may skip this chapter. Others will find it useful, as well as a convenient source for review.
Quite often, we are faced with problems that seem impossible to solve because they involve two or more unknowns. However, a solution can be found if we write two or more linear independent equations [*] with the same number of unknowns, and solve these simultaneously. Before we discuss generalities, let us consider a practical example.
Jeff Simpson plans to start his own business, manufacturing and selling bicycles. He wants to compute the break-even point; this is defined as the point where the revenues are equal to costs. In other words, it is the point where Jeff neither makes nor loses money.
Jeff estimates that his fixed costs (rent, electricity, gas, water, telephone, insurance etc.), would be around $1,000 per month. Other costs such as material, production and payroll are referred to as variable costs and will increase linearly (in a straight line fashion). Preliminary figures show that the variable costs for the production of 500 bicycles will be $9,000 per month. Then,
Let us plot cost ( y-axis), versus number of bicycles sold ( x-axis) as shown in Figure...
