Chapter 3 - Linear and Quadratic Functions - 3.1 Properties of Linear Functions and Linear Models - 3.1 Assess Your Understanding - Page 128: 43

a) $x=5000$ units b) $x>5000$ units

We are given: $R(x)=8x$ $C(x)=4.5x+17,500$ a) Find the break-even point: $R(x)=C(x)$ $8x=4.5x+17,500$ $8x-4.5x=4.5x+17,500-4.5x$ $3.5x=17,500$ $x=\dfrac{17,500}{3.5}$ $x=5000$ b) Find the number of units that must be sold to earn a profit: $R(x)>C(x)$ $8x>4.5x+17,500$ $8x-4.5x>4.5x+17,500-4.5x$ $3.5x>17,500$ $x>\dfrac{17,500}{3.5}$ $x>5000$