Question

The USAF is thinking of purchasing a improved automatic controller (no human required) at a cost of $100,000 that can make 4,000 target contacts per hour to replace USAF specialists that can, on average, make 1,000 target contacts per hour. Note that a USAF Specialist is paid a relatively low salary of $8/hour (but with good veteran benefits) and that the controller will require $1/hour maintenance costs. How many hours of target detection would it take to pay off this new controller?

Answer 1

Answer:

It would take 3225.8 hours of target detection to pay off the new controller

Explanation:

First, to find out how many hours it would take, we calculate what is the cost per contact for both options:

$\mbox{cost per contact}=\frac{\mbox{cost per hour}}{\mbox{contacts per hour}} \\\\\mbox{cost per contact}_{specialist} =\frac{8 \frac{\ }{h} }{1000\frac{contacts}{hour} } =8*10^{-3} \frac{\ }{contact}\\\\\mbox{cost per contact}_{controller} =\frac{1 \frac{\ }{h} }{4000\frac{contacts}{hour} } =2.5*10^{-4} \frac{\ }{contact}$

Knowing the cost per contact, we calculate savings per contact when using the controller:

$Savings=\mbox{cost per contact}_{specialist}-\mbox{cost per contact}_{controller}\\Savings=8*10^{-3} \frac{\ }{contact}-2.5*10^{-4} \frac{\ }{contact}=7.75*10^{-3} \frac{\ }{contact}$

Now that we know how much the automatic controller saves, we calculate how many contacts it would take to pay it off, and then, taking into account contacts per hour, how many hours:

$Hours=\frac{\mbox{cost of the controller}}{\mbox{savings per contact}}*\frac{\mbox{1}}{\mbox{contacts per hour}} \\\\Hours=\frac{\ 100000}{7.75*10^{-3} \frac{\ }{contact}} *\frac{\mbox{1}}{4000\frac{contacts}{hour} }}=3225,8 \mbox{ hours}$

That means, without taking into account veteran benefits (that raise the cost of the USAF specialist), it would take around 134 days of target detection to pay off the new controller.