Problem $1(20$ points$)$

Each month, a gas station sells $8,000$ gallons of gasoline. Each time the parent company refills the tanks it charges the station $\backslash (\backslash$$ $300\backslash )$ plus an additional $\backslash (70\backslash$$ $\backslash )$ per gallon. The annual cost of holding a gallon of gasoline is $404.$ Assume there is no lead time and using a basic EOQ model answer the following questions.

$($a$)$ How large should each order be$?$

$($b$)$ If the station orders the amount you calculated in part $($a$),$ how many orders per year will be placed?

$($c$)$ If the station orders the amount you calculated in part $($a$),$ how long will it be between orders?

$($d$)$ If the station orders the amount you calculated in part $($a$),$ what will be the average total cost per month $($include the cost per unit, $\backslash ($ c $\backslash$lambda $\backslash )$ term, in this total$)?$

Problem $2(15$ points$)$

For the basic EOQ model, use the formula $\backslash ($ Q$^\{*\}=\backslash$sqrt$\{\backslash$frac$\{2$ K $\backslash$lambda$\}\{$h$\}\}\backslash )$ to determine how $\backslash ($ Q$^\{*\}\backslash )$ would change in the case of each of the following changes in the costs or the demand rate. $($Consider each change independently.$)$

$($a$)$ The set up $($fixed$)$ cost becomes nine times as large as its original value.

$($b$)$ The demand rate is reduced to $36$ percent of its original value.

$($c$)$ The unit holding cost becomes nine times as large as its original value.