Question $1.$ Inventory $($Economic Order Quantity$)$

Tom, who is the manager at your favorite convenience store near McCombs, finds stocking jumbo bags of salty snacks $($potato chips, tortilla chips, pretzels etc.$)$ to meet the students late$-$night cravings to be a major headache. He is trying to figure out how to manage his inventory cost effectively. First, he looks at his regular potato chips invEntory

Average demand $=50$ bags$/$day$.$ Each bag cost $$5\mathrm{.}00$ to buy from his distributor. Tom sells the bags for $$10\mathrm{.}00$ each. Each time he places an order for snacks, his distributor charges him a $$100$ flat shipment rate. Tomfigures that the time it takes for one of his workers to determine how many snack bags to order and then put the bags on the shelves to be $45$ minutes per order. His junior workers earn $$20/$hour $($including fringe costs such as taxes and vacation$).$ The holding rate on property near McCombs is high at $30\%$ because space there is very expensive. Toms shop is open $7$ days$/$week$,365$ days$/$year$.$

$($a$)$ If Tom is optimizing his costs, how many bags should he order? $($Round down to the nearest integer.$)$

$($b$)$ How much does it cost to hold this inventory in dollars per year? $1(1$ pt$)(1$ pt$)$

$($c$)$ How many times does Tom order per year on average? $($You may end up with a non$-$integer answer such as $8\mathrm{.}62($note that $8\mathrm{.}62$ may not necessarily be the correct answer to this question$).$ Because it is an average, do not round the answer. As an example, if you did get an answer of $8\mathrm{.}62,$ do NOT round it to $9,$ but enter $8\mathrm{.}62$ into the box.

$($d$)$ Given that Tom places the number of orders per year as above, how much are his ordering costs per year? $($Note that this excludes his holding costs.$)$

$($e$)$ What are his total inventory management costs $($holding $+$ ordering costs$)$ per year for regular potato chips?

$($f$)$ Tom also sells $50$ bags of wavy potato chips per day, which have the same price and cost structure. He notices that his customers seem indifferent between the regular and wavy potato chips. So$,$ he thinks that he could take care of both his regular potato chip customers AND his wavy potato chip customers by stocking only regular potato chips. $($This would raise demand for regular potato chips to $100$ bags per day.$)$ If Tom does this, what would his new order quantity be$?(1$ pt$)(1$ pt$)2(1$ pt$)(1$ pt$)$

$($g$)$ What would his total inventory management costs $($holding $+$ ordering costs$)$ per year be if Tom adopts the policy in

$($f$)$ to only order regular potato chips?

$($h$)$ If you did this correctly, your answer above

$($g$)$ should be less than double your answer in

$($f$).$ In a couple of sentences, please explain why you think this happened. $($Graded on completion.$)$