Cigar Company Profits The daily profits of a cigar company from selling x cigars are given by

p(x) = -0.05x² + 100x - 2000

The government wishes to impose a tax on cigars (sometimes called a sin tax) that gives the company the option of either paying a flat tax of $10,000 per day or a tax of 10% on profits. As chief financial officer ((FO) of the company, you need to decide which tax is the better option for the company.

(a) On the same screen, graph Y₁ = p(x) - 10,000 and Y₂ = (1 - 0.10)p(x).

(b) Based on the graph, which option would you select? Why?

(c) Using the terminology learned in this section, describe each graph in terms of the graph of p(x).

(d) Suppose that the government offered the options of a flat tax of $4800 or a tax of 10% on profits. Which would you select? Why?