Mathematics

Problem

A company models its profit

P(x)

(in dollars) from selling

x

units with the piecewise function

P(x)=\begin{cases} 2x+5, & 0\le x<50,\\ ax+b, & 50\le x<80,\\ 10x-470, & x\ge80. \end{cases}

Find the values of

a

and

b

that make

P

continuous for all

x\ge0