Question

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?

Answer 1

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=TC_H=FC+X*VC=200+X

In case of shovel

Fixed cost=FC=$10 per year

Variable Cost=VC=$5 per car

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

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

TC_H=TC_S

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.