(a) Including equations and diagrams where appropriate, briefly explain how to select the optimum operating point of a single screw polymer processing extruder. Then, explain how to change/move this operating point across the process operating window. Also, provide the definitions of all the terms in the related equations. (b) You have been asked to choose a suitable technique to manufacture a hollow object using powdered polymer material. Also, it has been mentioned that the process should be simple and should not involve advanced process control requirements and compressed air due to the limitation of the facilities. With the help of a labelled sketch, describe a suitable manufacturing technique with its main stages. In your answer, mention two main disadvantages/limitations of the process. (c) With the aid of suitable sketches, briefly discuss three different types of die geometries used in the Chill-roll Casting of films. Then mention the two key advantages of this process compared to the Blown Film Extrusion process. (d) In injection moulding processes, the cooling time calculation is critical as it is a key factor in deciding the cycle time. The following equation is commonly used for this purpose (where all terms in the equation have their usual meaning). =T0TST(x)TS=Cexp(2Fo) Based on this equation and other related details, provide an equation for the cooling time (t) calculation. Then, briefly discuss how the cooling time can be affected with the changes to the Product Dimensions, Process Settings, and Materials; with a mention of which part/term of this equation is affected by each of these parameter changes. (e) With the aid of a labelled suitable sketch, briefly describe the Tadmor melting model related to single screw polymer extrusion