$$Sam$\text{'}$s Pet Hotel operates $50$ weeks per$$ year, $6$ days per$$ week, and uses a continuous review inventory system. It purchases kitty litter for $$$$13\mathrm{.}00$ per bag. The following information is available about these$$ bags:

followsDemandequals$75$bags$/$week

followsOrder costequals$$$$52\mathrm{.}00/$order

followsAnnual holding costequals$25$ percent of cost

followsDesired $$cycle$-$service levelequals$80$ percent

followsLead timeequals$2$ weeks $(12$ working$$ days$)$

followsStandard deviation of weekly demandequals$15$ bags

followsCurrent $$on$-$hand inventory is $320$bags$,$ with no open orders or backorders.

Part $2$

a$.$ Suppose that the weekly demand forecast of $75$ bags is incorrect and actual demand averages only $50$ bags per week. How much higher will total costs$$ be$,$ owing to the distorted EOQ caused by this forecast$$ error?

The costs will be $$$

$$

enter your response here higher owing to the error in EOQ. $($Enter your response rounded to two decimal$$ places.$)$