## Problem of the Day #200: Chocolate Wrapping
*October 5, 2011*

*Posted by Saketh in : potd , trackback*

Lucy and Ethel work at a chocolate factory. They sit at a conveyer belt and wrap passing chocolates in silver foil. The volume of chocolate moving through is associated with the function

$$f(t) = |t^2 – 2at – a^2 – \frac{3}{4}|$$

where $t$ ranges from $0$ at the start of the day to $1$ at the end. Lucy and Ethel can only keep up if $f(t) \leq 1$ at all times. Determine the greatest value of $a$ for which they will make it through the workday.

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