Truck Alpha initially costs 410 more than Truck Beta but it

Truck Alpha initially costs $410 more than Truck Beta, but it consumes 0.03 liter/km versus 0.07 liter/km for Beta. Both trucks last 9 years, and Beta\'s salvage value is $123 smaller than Alpha\'s. Fuel costs $1.98 per liter. Other things being equal, beyond how many kilometers of use per year does Alpha become preferable to Beta? Enter your answer as follows: 12345.67

Solution

Here let total kilometer alpha use be x.

So as per the language given,

Total liters by alpha = 0.03x

so total consumption by alpha = 1.98 * 0.03x = $0.0594x

and total liters by beta = 0.07x

so total consumption by beta = 1.98 x 0.07x = $0.1386x

Again let total cost of Beta=y

so total cost of alpha = 410+y

And total salvage cost of beta = 410+y-123 = 287+y

Now for alpha to be preferred , its total cost must be greater than beta

or

So total cost of alpha = $(410 +y+ 0.0594x) and total cost of beta = 287+y+ 0.1386x

Now for better performance by alpha, we have

0.1386x +y+287 > 410+y+0.0594x

or 0.1386x-0.0594x > 123

or 0.0792x > 123

or x >123/0.0792 = 1553