set up fee is always there so there is always 50 starting feee
first 50 shirts means every shirt up to and including the 50th shirt cost 7.99 each
any number past that (51st shirt and beyond) is 6.99
40 shirts
this is 50 and below and also add set up fee
50+407.99=$369.60
$369.60 for 40 shirts
80 shirts
this is above 50, BUT, the first 50 are still 7.99 each, the rest are 6.99
80-50=30
don't forgeet set up fee
so
50+507.99+306.99=659.20
cost for 80 shirts is $659.20
piecewise function
y=mx+b form is nice
first part is easy (x≤50 part)
y=7.99x+50
for the bit that is over the 50, we have to include the 50 shirts in the b
507.99=399.50
and the setup is 50 so add that also
399.50+50=449.50
and subtract the 50 from x
y=6.99(x-50)+449.50
therefor the piecewise functin is
\(f(x)= \left \{ {x \ \textgreater \ 50, {y=6.99(x-50)+449.50} \atop x \leq50, {y=7.99x+50}} } \right\)
