$$Sam$\text{'}$s Pet Hotel operates

$5252$

weeks per$$ year,

$66$

days per$$ week, and uses a continuous review inventory system. It purchases kitty litter for

$$$$12\mathrm{.}5012\mathrm{.}50$

per bag. The following information is available about these$$ bags:

follows$$Demandequals$=8080$

$$bags$/$week

follows$$Order

costequals$=$$$55\mathrm{.}0055\mathrm{.}00/$order

follows$$Annual

holding

costequals$=3535$

percent of cost

follows$$Desired

$$cycle$-$service

levelequals$=8080$

percent

follows$$Lead

timeequals$=44$

weeks

$(2424$

working$$ days$)$

follows$$Standard

deviation of weekly

demandequals$=1515$

bags

follows$$Current

$$on$-$hand inventory is

$320320$

$$bags$,$ with no open orders or backorders.

Part $2$

a$.$ Suppose that the weekly demand forecast of

$8080$

bags is incorrect and actual demand averages only

$5555$

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.$)$