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 is also possible for Rex to buy a high-quality hydraulic car smasher that cost $450 per year to own and if with this smasher he could dispose of cars at a cost of $.80 per car, it would be worthwhile for him to buy this high-quality smasher if he planned to dispose of
A)at least 1,260 cars per year.
B)at least 1,250 cars per year.
C)no more than 625 cars per year.
D)no more than 1,250 cars per year.
E)at least 625 cars per year.

Question

Quizplus · Accepted Answer

To determine if it is worthwhile for Rex to buy the high-quality hydraulic car smasher, we need to compare the cost of disposing of cars with this smasher to the cost of disposing of cars with the other options. Option 1: Buy a shovel and pay his brother to bury the cars. Cost per car = $10 (shovel) + $5 (brother's fee) = $15 Option 2: Buy a low-quality car smasher. Cost per car = $200 (annual cost) / total cars smashed + $1 (marginal cost per car) Let's say x is the number of cars Rex smashes per year. Cost per car = ($200/x) + $1 Option 3: Buy a high-quality hydraulic car smasher. Cost per car = $450 (annual cost) / total cars smashed + $0.80 (marginal cost per car) Again, let's say x is the number of cars Rex smashes per year. Cost per car = ($450/x) + $0.80 We want to find the point at which option 3 becomes cheaper than option 1 or 2. In other words, we want to find the point at which the cost per car for option 3 is less than $15 or ($200/x) + $1. ($450/x) + $0.80 < $15 and ($450/x) + $0.80 < ($200/x) + $1 Solve for x: ($450/x) + $0.80 < $15 ($450/x) < $14.20 x > 450/14.20 x > 31.7 (rounded up) ($450/x) + $0.80 < ($200/x) + $1 ($250/x) < $0.20 x > 1250 Therefore, it is worthwhile for Rex to buy the high-quality hydraulic car smasher if he plans to dispose of at least 31.7 (rounded up) cars per year, but it becomes the best choice if he plans to dispose of at least 1,250 cars per year. Thus, the answer is B.

Rex Carr Could Pay $10 for a Shovel That Lasts