Question

A producer of perishable product offers a wage incentive to the drivers of its trucks. A 

standard delivery route takes an average of 20 hours. Drivers are paid at the rate of $10 per 

hour up to a maximum of 20 hours (if the trip requires 30 hours, the drivers receives payment 

for only 20 hours). There is an incentive for drivers to make the trip in less than 20 hours. for 

each hour under 20, the hourly wage increases by $1. Assume x equals the number of hours 

required to complete the trip. 

(a) Determine the function w = f(x), where w equals the hourly wage in dollars

(b) Determine the function which states the driver’s salary for the trip as a function of x.

(c) What trip time x will maximise the driver’s salary for the trip

(d) What hourly wage is associated with this trip time?

(e) What is the maximum salary?

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.