Chapter 1 - Section 1.2 - Functions and Models - Exercises - Page 72: 27

5000 units

Cost $=$ Variable cost $+$ Fixed cost If $R(x)$ is the revenue from selling $x$ items at a price of m each, then $R$ is the linear function $R(x)=mx$ . Profit $=$ Revenue-Cost,$\qquad P(x)=R(x)-C(x)$ Breakeven occurs when $P=0$, or $R(x)=C(x)$. ------------------- We first express $R(x)=2x$ Since Variable cost = $0.4\cdot R(x)=0.4(2x)=0.8x$, the Cost function is $C(x)=0.8x+6000$ Breakeven$: R(x)=C(x)$ $2x=0.8x+6000\qquad/-0.8x$ $1.2x=6000\qquad/\div 1.2$ $x=5000$ To break even, there should be 5000 units sold