6. You are a design engineer for an automaker who is trying to reduce the comple
ID: 3072855 • Letter: 6
Question
6. You are a design engineer for an automaker who is trying to reduce the complexity of manufacturing its cars and thus improve quality and cut costs in its manufacturing. Currently, the vehicle you helped design has 10 different options (sunroof, enhanced stereo, paint colors (white, black, red, silver, gold, or green), spoiler, and a turbo engine). When cars are ordered, dealers can select any of the colors (though only 1 per car) and any or no options for each vehicle (5 points). (a) How many ways can dealers select options for cars? (b) The company decides that if they reduce the number of ways cars can be ordered their plant would increase efficiency significantly, but they don't want to eliminate any of the offered options. You have some good ideas on how to change the way cars can be ordered, here is what you come up with: to have a sun roof, stereo, and any color paint. metallic paint (no silver or gold) paint color, a sunroof, and enhanced stereo. (i) The "turbo sport" package: A turbo engine and a spoiler then the dealer/customer can choose (ii) The "basic" edition: No turbo, no spoiler, no sunroof, no enhanced stereo and only hon (ii) The "basic plus" edition: No turbo, no spoiler, but the dealer/customer can choose any How many ways can vehicles be ordered now?Explanation / Answer
a)
number of ways =N(2choice (yes or no) for sunroof and 2 for enhanced stereo , 6 for colors 2 for spoiler and 2 for turbo engine)=2*2*6*2*2=96
b)
number of ways =N(ways to choose turbo sport )+N(ways to choose Basic edition)+N(ways to choose basic plus edition)=(2*2*6)+4+(6*2*2)=52
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