Processing the Processor

Calculus Level 3

processor

$N$ characters of information are held on a magnetic tape in batches of $x$ characters each, the batch processing time being $A+Bx^{2}$ seconds where $A$ and $B$ are constants. The optimal value of $x$ for fast processing is $\text{\_\_\_\_\_\_\_\_\_\_}$ .

\sqrt{\frac{A}{B}}

\sqrt{\frac{B}{A}}

\frac{A}{B}

\frac{B}{A}

B

None of these choices

A

1 solution

Sparsh Sarode
May 24, 2016

Suppose that there are n batches. So the total number of characters to be processed $N=nx$

$n=\frac{N}{x}$

Total time taken to process N characters:

$t=n(A+Bx^{2})$

$t=\frac{N}{x}(A+Bx^{2})$

On differentiating wrt x and equating it to 0:

$x=\sqrt{\frac{A}{B}}$

Processing the Processor

1 solution

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