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In 2017 12.5 billions packs of 20 cigarettes/pack were sold in the United States at an average price of $8.00 a pack. Economic studies have found that a 10% increase in cigarette prices causes about a 5% decrease in cigarette consumption. Smoking-related illness in the United States cost more than $300 billion each year. The government wants to reduce smoking as much as possible. What would have a greater impact on reducing cigarette consumption: a) increasing tax on cigarettes by $2.00 per pack or b) placing a quota of 10 billion packs per year on the production of cigarettes? Why? (2 points)

Suppose there is a bill to increase the tax on cigarettes by $1 per pack coupled with an income tax cut of $500. Suppose a person smokes an average of 500 packs of cigarettes per year—and would thus face a tax increase of about $500 per year from the cigarette tax at the person’s current level of consumption. The income tax measure would increase the person’s after-tax income by $500.

Would the combined measures be likely to have any effect on the person’s consumption of cigarettes? Why or why not?

Find the equation of the plane through the point 𝑃=(3,4,4)�=(3,4,4) and parallel to the plane 2𝑥−3𝑦−3𝑧=5.