Chapter $12$ Dynamic Programming

$-42-24.$ Mr sond age $13,$ has a lawn $-$mowing business with $10$ customers. For each customer, he cuts the grass $3$ times a year. which earns him $\backslash (\backslash$$ $50\backslash )$ for each mowing. He has just paid $\backslash (\backslash$$ $200\backslash )$ for a new mower. The maintenance and operating cost of the mower is $\backslash (\backslash$$ $120\backslash )$ for the firs year in service and increases by $\backslash (20\backslash \%\backslash )$ a year thercafter. A $1-$year$-$old mower has a resale value of $\backslash (\backslash$$ $150\backslash ),$ which decreases by $\backslash (10\backslash \%\backslash )$ a year thereafter. My son, who plans to kecp his kssiness until he is $16,$ thinks that it is more economical to buy a new mower even $2$ years He bases his decision on the fact that the price of a new mower will increase only by $\backslash (10\backslash \%\backslash )$ a year. Is his decision justified?