Question

N characters of information are held on a magnetic tape in batches of x characters each, the batch processing time being (a + bx²) seconds, where a and b are constants. The optimal values of x for fast processing, is –

• A. $\frac { \alpha } { \beta }$
• B. $\frac { \beta } { \alpha }$
• C. $\sqrt { \frac { \alpha } { \beta } }$
• D. ) $\sqrt { \frac { \beta } { \alpha } }$

Answer 1

Answer: (C)

$\sqrt { \frac { \alpha } { \beta } }$

Answer 2

Total time taken in processing all batches

T = (a + bx²) Ž T = + Nbx

= – + Nb

For maximum or minimum

= 0

Ž x₀ = $\sqrt { \frac { \alpha } { \beta } }$ ; = + > 0

So, minimum time for processing, x₀ =$\sqrt { \frac { \alpha } { \beta } }$.