Question

A producer of perishable product offers a wage incentive to drivers of its truck. A standard delivery
takes an average of 20 hours. Drivers are paid at the rate of $15 per hour up to a maximum of 20 hours.
If the trip requires more than 20 hours, the drivers receive compensation for only 20 hours. There is
an incentive for drivers to make the trip in less (but not too much less!) than 20 hours. For each hour
under 20, the hourly wage increase by $2.5.
(a) Determine the function w =f(x) where w equals the hourly wage in dollars and x equals the
number of hours required to complete the trip.
(b) What trip time x will maximize the drivers salary for a trip?
(c) What is the hourly wage associated with the trip time?
(d) What is the maximum salary?
(e) How does this salary compare with that received for a 20-hour trip?

Answer 1

(a)

$$w=f(x) = \begin{cases} 0 & x<0 \\ (15+2.5)\lfloor{x}\rfloor &0\leq x <20\\ 300 &x\geq20 \end{cases}$$

(b),

If $19\leq x<20, w(x)$ has maximum

(c) in

We consider $w$ as the hourly wage associated with the trip time in dollars.

(d)

If $19\leq x<20, w(x)$ has maximum in $332.50

(e)

$$\$332.50>\$300$$

The maximum salary is greater than salary received for a 20-hour trip.