$(8)$ Consider the following demand distribution for a perishable product. The product

costs $$1\mathrm{.}5,$ sells for $$3\mathrm{.}6$ and has a salvage value of $$0\mathrm{.}99.$

$($i$)$ What is the expected profit if $40$ units of the product are ordered? $(10)$

$($ii$)$ Complete the column for cumulative probability distribution and determine

the optimal order quantity? $(15)$

$(9)$ ABC Chocolatiers place their orders for boxes of a Belgian brand of chocolate

every three weeks $($twenty$-$one days$).$ Lead time to shipment is FOUR days.

Daily demand is normally distributed with a mean of $20$ boxes and a standard

deviation of six boxes; the company has a service$/$fulfillment policy of $97\%.$ The

manager is about to place order for the next period: how many boxes should she

order if they currently have $78$ boxes in the store?$(10)$ If inventory turnover rate is $15,$ how long does it take on average for a

piece of inventory to sell? Assume $360$ working days. $(7)$

$(11)$ Calculate the inventory turnover rate given that the annual revenue is

$$420,000$; prices are set with a markup of $20\%$ on cost$.$ The beginning and

ending inventory were found to be $$23,000$ and $$17,000$ respectively. $(10)$

$(12)$ A company has an annual sale of $$500,000$;$80\%$ of the sale is credit

sales. Beginning and ending accounts receivables are respectively $$13,000$ and

$$19,000.$ What is the accounts receivable turnover ratio. $(8)$

$(13)$ The following data is available for a company.

Other $$5,000$

$($a$)$ Calculate the single factor productivity for capital. $(5)$

$($b$)$ Calculate the multifactor productivity for labor, raw materials and energy.

$(10)$

$($c$)$ Calculate the overall productivity. $(10)$