SOLUTION: ) A builder must decide whether to rent or buy an excavating machine. If he were to rent the machine, the rental fee would be €600 per month, and the daily cost (gas, oil, and dr

Question 1198749: ) A builder must decide whether to rent or buy an excavating machine. If he were to rent the machine, the rental fee would be €600 per month, and the daily cost (gas, oil, and driver) would be €60 per day it is used. If he were to buy it, his fixed annual cost would be €4,000, and the daily operating and maintenance costs would be €80 per day the machine is used. What is the least number of days each year that he would have to use the machine to justify renting rather than buying it?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rent = 600 per month plus 60 for each day it is used.
buy = 4,000 per year plus 80 for each day it is used.

the yearly cost for renting is equal to 600 * 12 = 7200 plus 60 for each day it is used.

the yearly cost for buying is 4,000 plus 80 for each day it is ued.

your inequality is 7200 + 60x < 4000 + 80x
x is the number of days.
subtract 4000 from both sides of the equation and subtract 60x from both sides of the equation to get:
3200 < 20x
divide both sides of the equation by 20 to get:
160 < x

the machine would have to be used more than 160 days for the rental option to be cheaper than the buy option.

at 160 days, the rental option is 7200 + 60 * 160 = 16800
at 160 days, the buy option is 4000 _+ 80 * 160 = 16800

that'a the break even point.

at 161 days, the rental option is 7200 + 60 * 161 = 16860
at 161 days, the buy option is 4000 + 80 * 161 = 16880
the rental option is cheaper than the buy option by 20.

at 300 days, the rental option is 7200 + 60 * 300 = 25200
at 300 days, the buy option is 4000 + 80 * 300 = 28000.
the rental option is cheaper than the buy option by 2800.

2800 / (300 - 160) = 2800 / 140 = 20.
the rental option is cheaper than the buy option by 20 dollars for each day over 160.

the equations can be graphed as shown below:

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