In this exercise we will show that the Boolean product of zero–one matrices is associative. Assume that A is an m × p zero–one matrix,B is a p × k zero–one matrix, and C is a k × n zero–one matrix. Show that A⊙ (B⊙C) = (A⊙B) ⊙C.
PKSC final exam review CORRECT TESTS!!! EVALUATION FOR EXTRA CREDIT *** VAUGE review from prof HISTORY - Know timeline dates - Three M’s in definition of packaging (materials, methods, machinery) - Ancient and man-made packages - Industrial revolution o Can, celluloid, paperboard cartons - Late 20 century o 50’s 60’s, 70s, 80s, 90s - Trends - users and suppliers o users: consumer, industrial, institutional o suppliers: converters, machinery and services FUNCTIONS - contain - protect - inform/sell - utility of use* NOT IN TEXTBOOK - four levels o primary, secondary, tertiary, and quaternary - product o contents, environment, damage - inform/sell: o required, motivational, trade dress - utility of use: o consumer, retailer, shipper/distributer MATERIALS - paper and paper board – wood pulp, cellulose - metals o steel o aluminum - glass - plastic - paper o cellulose and lignin o thickness: paper vs paperboard 0.12” point .014” = 14 point o what “plastic” comes from wood Cellophane o three ways to make pulp Mechanical, chemical, and semi-chemical o general procedure for paper/paperboard Screen, squeeze and dry o Callenderig o Basis weight of paper o Etc. o Use for bending grade board o Three basic design styles for folding cartons o Tube, tray and hybrid - Testing Mulllen bursts and edge crush test - RSC Regular slotted container - Two basic styles of composite cans o Convolute and - METALS o Cans- steel and aluminum o Two basics kind of can: three and two pieces o Etc. o Plating weights measured in lbs/basebox o Three ways to seal the side seam of a three piece can Weld, solder or adhesive o Bayer process – bauxite ot aluminum o Hall herlout process o Now thin is aluminum foil 6 mil o Is aluminum used for packaging as a pure metal NO o What happens to WVTR as thickness of foil decreases Why Increases bc pinholes - GLASS o How to make glass bottles Blow and blow, press and blow o Major ingredients o What is cullet o Two methods for making glass bottles o What is gob o What is annealing Why important o Parts of a bottle o Advantages/disadvantage - POLYMERS o What is gutta percha o What is the first synthetic plastic Bakelite o Etc. o Name of chem reaction used to link monomers Polymerization o If you link different monomers o Know abbrev : HDPE, LDPE, PP, PET, PVC, PVDC(saran) o What is density Yield How related o Thermoset/thermoplastic o Cost- more specialized plastics are more costly Since the basic structure of most common polymers are similar, what mades each one different Side chains o What basic process is used for all types of forming methods Extrusion – melting plastic o What are 2 ways to make film Cast and ring die o What does orientation meant as it relates to film Stretched to align molecules for strength o What is coextrusion and what is it used for Blends different polymers, film, sheet and bottles o What is injection molding used for o What type of package does extrusion blow molding produce Bottle o What is a parison Hollow tube inflatd into bottle o How is wall thickness controlled during extrusion blow molding Programmed parison o What types of package are made by injection bow molding Bottles o Stretch blow molding Bottles o What are two advantages of extrusion bow ad molding compare to IBM and ISBM One mold and handles o Adv. And disadv. - FORMS o Rigid – glass bottle o Semi rigid - squeeze ketchup bottle o Flexible – bread bag or potato chip bag o Types of closures, indention seal, child resistant, tamper resistant, decorative etc o Dimensional analysis – what is meant when the film converter…. o Properties of laminates: structural barrier o Two ways to form a pouch: V/F/F/S and H/F/F/S o How perrmiation happens o Levels of packaging Primarty secondary tertiary quaternary o What are 3 basic areas of testing Quality, environmental, shipping and abuse (distribution and transportation) o Know the areas of testing and the specific tests o Know how to solve problems relating to stacking strength PACKAGE MACHINERY - Line function - Line speed - What really counts Output - Know how to solve problems related to lines peed - What are 2 main types of fillers o Constant level o Constant volume - How do they differ GRAPHICS AND PRINTING - Package design consists of two components… - Three fundamental messages a package must anser o What is this o What will it do fo rme o Who guarentees this - 4 basic methods of printing - What are the 4 types of package development projects - What are two development paths for pkg development DEVELOPMENT - Wht oart of a company drives development PACKAGING LAWS AND REGS - CFR - Laws and regs form all years ENVIROMENTAL LAWS AND REGULATIONS - What are the 2 main types of environmental laws and regs o Health laws – fed o Enviro – state and local o Man laws indirectly related to pkg o Mandatory recycling laws o Know modification for packaging Degradable, high cone, pull tabs - Packaging is the largest contributor of solid waste 30% - Wht is solid wastes hierarchy or disposal - Know the plastic recycling codes (1-7) - What does innovation do o Boost sales o Changes consumers demands o Change with tech developments - What is the # one factor driving innovation o Convenience!