Consider an e-shop that sells consumergoods to the public and processes incoming customer orders in two stages: - Stage 1: Order is received and confirmed at warehouse. Order is picked and packed. - Stage 2: Invoice and shipping bill is prepared. Order is dispatched. The following figure is a stock and flow diagram of the order processing procedure: stage-1 orders stage-2 orders arrival rate stage-1 exit rate shipment rate The stocks "stage-1 orders" and "stage-2 orders" are the numberof currently processed orders in stage 1 and 2, respectively. "Arrival rate" is the rate at which customer orders arrive at the e-shop. "Stage-lexit rate" is the rate at which stage-1 orders are forwarded to the next stage. "Shipment rate" is the rate at which processed orders are shipped to customers. Stage 1 and stage 2 are pipeline delays with delay times D1 = 2 days and D2 =1 day, respectively. Initially, the "arrival rate", "stage-1 exit rate" and "shipment rate" are equal to 0. Initially, both stocks "stage-1 orders" and "stage-2 orders" are equal to 0. The "arrival rate" is equalto 25 orders/day for day t = 3, 4, 5, 6, 9, 10, 11, 12 and 0 elsewhere (see figure below): prders/day 25 2 3 4 5 6 7 8 9 10 11 12 13 ...... days Question 1.1 (15 %) Calculate the "stage-1 exit rate" and the "shipment rate" for day 0 to 15. Question 1.2 (15 %) Calculate the net change rate for stocks "stage-1 orders" and "stage-2 orders" for day O to 15. Question 1.3 (20 %) By means of graphical integration, calculate and plot the values of "stage-1 orders" and "stage-2 orders" for day 0 to 15.