Kate's Mini-Mart uses a periodic review, order-up-to inventory model to manage inventory, for one of their more popular products, Tofu Jerky, Kate (the owner) insists on maintaining an 80% cycle service level. Kate buys Tofu Jerky for $1.00 per pack and it sells for $1.40. it costs Kate $0.10 per pack per week to hold inventory. The supplier has a 4-week lead time (with no randomness). Average demand expects to be 55. (Please use the Gamma distribution to model demand during the exposure period.) Suppose Kate orders every week (and uses the 80% CSL mentioned above). What is the fill rate?

do it fast