You can either do your own yard work or you can pay someone to do it for you.
You find that it takes you about 50 minutes to clip, mow, and otherwise clean up your yard each time you do it.
You do it four times each month.
Also, once a month you need to maintain the lawn equipment. That takes about 49 minutes in addition to you clipping, mowing, etc.
All of the maintenance and lawn work must be done on a Saturday because of your typical work schedule.
You are paid $ 18.75 hourly and get time and a half on weekends.
Alternatively, you can pay someone $ 50 monthly to do the work for you.
(a) Assume that your off-time has value at the rate you are normally paid. What is the monthly cost of your lawn care when you do it yourself and have no chance for weekend work?
(b) Assume that you have the option to work the weekend time you need to spend on your yard. So you must pay someone to do the yard work.
You should assume your overtime rate applies here.
What is the net gain to you to pay someone to do the clean-up for you?
(a) To calculate the monthly cost of your lawn care when you do it yourself and have no chance for weekend work, we need to consider the time spent on yard work and lawn equipment maintenance.
Time spent on yard work per month = 50 minutes per session x 4 times per month = 200 minutes per month
Time spent on lawn equipment maintenance per month = 49 minutes per month
Total time spent on yard work and maintenance per month = 200 minutes + 49 minutes = 249 minutes
Now, let's calculate the cost of your time spent on yard work and maintenance:
Hourly rate = $18.75
Total cost of your time spent on yard work and maintenance = (249 minutes / 60) hours x $18.75 per hour
Let's compute:
Total cost = (249 / 60) x 18.75 = $77.81
Therefore, the monthly cost of your lawn care when you do it yourself and have no chance for weekend work is approximately $77.81.
(b) To calculate the net gain to you by paying someone to do the clean-up for you and work the weekend time instead, we need to compare the cost of paying someone to do the work with the overtime pay you would earn by working during that time.
Cost of paying someone to do the work = $50 per month
Time spent on yard work and maintenance per month = 249 minutes
Overtime rate = Time and a half your regular rate = $18.75 x 1.5 = $28.13 per hour
Net gain = Overtime pay earned - Cost of paying someone
Overtime pay earned = (249 minutes / 60) hours x $28.13 per hour
Let's compute:
Overtime pay earned = (249 / 60) x 28.13 = $116.02
Net gain = $116.02 - $50 = $66.02
Therefore, the net gain to you by paying someone to do the clean-up for you is approximately $66.02.
To find the monthly cost of your lawn care when you do it yourself and have no chance for weekend work, we need to calculate the total time spent and multiply it by your rate of pay.
(a) Monthly cost when you do it yourself:
Time spent on yard work per month = 4 times * 50 minutes = 200 minutes = 3 hours and 20 minutes
Time spent on lawn equipment maintenance = 1 time * 49 minutes = 49 minutes = 0.82 hours
Total time spent = 3.2 hours + 0.82 hours = 4.02 hours
Since you have no chance for weekend work, you won't receive any additional payment for this time. Therefore, your monthly cost is the amount of time spent multiplied by your hourly rate.
Monthly cost when you do it yourself = 4.02 hours * $18.75/hour = $75.45
So the monthly cost of your lawn care when you do it yourself and have no chance for weekend work is $75.45.
(b) To find the net gain to you for paying someone to do the clean-up for you, we need to compare the cost of paying someone with the potential earnings from working during that time.
Monthly cost of paying someone = $50 (as given in the question)
Now, let's calculate the potential earnings if you choose to work during that time and get paid at your overtime rate.
Time spent on yard work and equipment maintenance = 3.2 hours + 0.82 hours = 4.02 hours
Overtime hourly rate = $18.75 * 1.5 = $28.125/hour
Potential earnings = 4.02 hours * $28.125/hour
Net gain = Potential earnings - Cost of paying someone
Net gain = (4.02 hours * $28.125/hour) - $50
Simplifying further,
Net gain = $112.8525 - $50
Net gain = $62.8525
So the net gain to you to pay someone to do the clean-up for you is $62.85.