Reconsider the bolt example in Problem $4.$ Suppose that although we have estimated demand to be $60$ per week, it turns out that it is actually $120$ per week $($i$.$e$.,$ we have a $100$ percent forecasting error$).$

$($a$)$ If we use the lot size calculated in the previous problem $($i$.$e$.,$ using the erroneous demand estimate$),$ what will the setup plus holding cost be under the true demand rate?

$($b$)$ What would the cost be if we had used the optimum lot size?

$($c$)$ What percentage increase in cost was caused by the $100$ percent demand forecasting error? What does this tell you about the sensitivity of the EOQ model to errors in the data?