MECH 431

Lesson 4 Practice Problems

Updated 2018-05-28

Lesson 4 Practice Problems

Problem 1

You are considering automating a test system you operate. You have two options: partial, or full automation. Partial automation will require you to spend 110 hours developing the system, and will save you 10 hours per month thereafter.

Full automation will require 200 hours of your time to develop, but save you 15 hours per month.

Your employer pays $40 per hour for you, all included. If they have a maximum acceptable payback period of 12 months, which option should they select?

Answer:

Assuming that we start the payback period immediately after the automation system is developed.

For partial automation: The total development cost is 110 hours \(\times\) $40 per hour which gets us $4400 of expense. The total benefit is 12 months \(\times\) 10 hours saved per month \(\times\) $40 per hour which is $4800. A net benefit of +$400 and benefit-cost ratio of \(\frac{4800}{4400}=\)1.09.

For full automation: Total development cost in this case is 200 hours \(\times\) $40 per hour equals $8000. The total benefit is 12 months \(\times\) 15 hours saved per month \(\times\) $40 saved per hour which is $7200. If we go with full automation, we are at a loss!

Therefore partial automation is the way to go.

Problem 2

Using an 18 month timeframe, estimate the benefit/cost ratio for each option (full or partial automation). Which option would you choose in this case?

Answer:

Just re-compute the above calculation but with 18 months. For partial automation, we get cost-benefit ratio of:

\[\frac{18\times10\times40}{4400}=1.64\]

For full automation:

\[\frac{18\times15\times40}{8000}=1.35\]

Here we see that partial automation is still the better option.