Question

# Rex owns a junk yard and can use one of two methods to destroy cars. The...

Rex owns a junk yard and can use one of two methods to destroy cars. The first method involves purchasing a hydraulic car smasher that costs \$200 a year to won and then spending a \$1 for every car smashed into oblivion; the second method involves purchasing a shovel that will last a year and costs \$10 and then paying his brother, Scoop, to bury cars at a cost of \$5 each

What is the smallest number of cars per year where for which it would pay Rex to buy the hydraulic smasher?

Let x cars are destroyed in a year.

In case of hydraulic car smasher

Fixed cost=FC=\$200 per year

Variable Cost=VC=\$1 per car

Total Cost=TCH=FC+X*VC=200+X

In case of shovel

Fixed cost=FC=\$10 per year

Variable Cost=VC=\$5 per car

Total Cost=TCS=FC+X*VC=10+5X

Let us equate both total costs to get the value of X which makes costs in both cases equal.

TCH=TCS

200+X=10+5X

4X=190

X=190/4=47.50

So, we can say that a minimum of 48 cars per year are needed to be destroyed to make the purchase of hydraulic car smasher attractive.

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