show ans and step! 26. Rex Carr could pay $10 for a shovel that lasts one year a
ID: 1214922 • Letter: S
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show ans and step!
26. Rex Carr could pay $10 for a shovel that lasts one year and pay $5 a car to his brother Scoop to bury the cars, or he could buy a low-quality car smasher that costs $200 a year to own and that smashes cars at a marginal cost of $1 per car If it were also possible for Rex to buy a high-quality hydraulic car smasher that cost $650 per year to own and if with this smasher he could dispose of cars at a cost of $(2/3 per car, it would be worthwhile for him to buy this high-quality smasher if he needed to dispose of a. at least 1,350 cars per year b. no more than 675 cars per year c. at least 1,360 cars per year d. no more than 1,350 cars per year e. at least 675 cars per yearExplanation / Answer
There are three methods of disposal with three different cost structure:
The last one will be worthwhile to have if the annual cost incurred on it is lowest
Compare and find the optimum x
200 + x > 650 + 2/3x
1/3x > 450
x > 1350
Second comparison
10 + 5x > 650 + 2/3x
13/3x > 640
x > 147
This means the optimum numbers of cars should be at least 1350 per year so that the third method of disposing cars become worthwhile to use. Consider x = 1351, annual cost in first method is $6765, in second method, it is $1551 and in third it is $1550.66. Hence option D is not the correct one.
Hence option A is correct.
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