QUESTION $5$

$(20$ Marks$)$

$5\mathrm{.}1$ Moses Mabhida Stadium is situated at the heart of KwaZulu Natal's economic hub. It has a conference

$(4$ Marks$)$ center that is capable of handling $1,500$ participants. However, conference management personnel believe that only $1,300$ participants can be handled effectively for most events. The last music event hosted, although forecasted to have $1,300$ participants, resulted in the attendance of only $1080$ participants. Determine efficiency and utilisation for the conference facility.

$5\mathrm{.}2$ Checkers Hyper in Rosebank sells $175$ units per month of OMO $5$ kg washing powder. The unit cost of

$(16$ Marks$)$ this product to the store is R$2\mathrm{.}50$ and the cost of placing an order has been estimated to be R$12\mathrm{.}00.$ Checkers Hyper uses an inventory carrying charge of $I=27\%$ per year. Provided this information, calculate $($a$)$ the optimal order quantity, $($b$)$ the order frequency, and $($c$)$ the annual holding and setup cost. If$,$ through automation of the purchasing process, the ordering cost can be cut to R$4\mathrm{.}00,$ what will be $($d$)$ the new economic order quantity, $($e$)$ the order frequency, and $($f$)$ annual holding and setup costs? Explain these results.