TAOCP 7.2.2.2 Exercise 147

Exercise 147. [05] [05] Evaluate $C_{\max}$ in (66) for $d = 0, 1, 10, 20, 30$, using the default $C_0$ and $C_1$.

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By equation (66), the cutoff value is

$$ C_{\max}=C_0+C_1d . $$

Using the default values $C_0=1000$ and $C_1=100$, we substitute each requested value of $d$.

For $d=0$,

$$ C_{\max}=1000+100(0)=1000 . $$

For $d=1$,

$$ C_{\max}=1000+100(1)=1100 . $$

For $d=10$,

$$ C_{\max}=1000+100(10)=2000 . $$

For $d=20$,

$$ C_{\max}=1000+100(20)=3000 . $$

For $d=30$,

$$ C_{\max}=1000+100(30)=4000 . $$

Therefore the requested values are

$$ \boxed{C_{\max}(0)=1000,\quad C_{\max}(1)=1100,\quad C_{\max}(10)=2000,\quad C_{\max}(20)=3000,\quad C_{\max}(30)=4000.} $$