$$Sam$\text{'}$s Pet Hotel operates $49$ weeks per$$ year, $7$ days per week. It purchases kitty litter for $ $6\mathrm{.}50$ per bag. The following information is available about these$$ bags:

followsDemand $=75$bags$/$week

followsOrder cost$=$$$70/$order

followsAnnual holding cost$=22$ percent of cost

followsDesired $$cycle$-$service levelequals$90$ percent

followsLead time$=2$week$($s$)(14$ working$$ days$)$

followsStandard deviation of weekly demand$=6$ bags

followsCurrent $$on$-$hand inventory is $200$bags$,$ with no open orders or backorders.

Suppose that$$ Sam's Pet Hotel uses a P system. The average daily$$ demand, d overbar$,$ is $11$ bags $(75/7),$ and the standard deviation of daily$$ demand, StartFraction Standard Deviation of Weekly Demand Over StartRoot Days per Week EndRoot EndFraction

$,$ is $2\mathrm{.}268$ bags. Refer to the standard normal tableLOADING... for$$ z$-$values.

Part $2$

a$.$ What P$($in working$$ days$)$ and T should be used to approximate the cost$$ trade$-$offs of the$$ EOQ?

The time between$$ orders, P$,$ should be

$$

$56$ days. $($Enter your response rounded to the nearest whole$$ number.$)$

Part $3$

The target$$ inventory, T$,$ should be

$$

$770$ bags. $($Enter your response rounded to the nearest whole$$ number.$)$

Part $4$

b$.$ How much more safety stock is needed than with a Q$$ system?

$$

$11$ bags. $($Enter your response rounded to the nearest whole$$ number.$)$

Part $5$

c$.$ It is time for the periodic review. How much kitty litter should be$$ ordered?

$$

enter your response here bags. $($Enter your response as an$$ integer.$)$