Competition: Two friends enjoy competing with each other to see who has the best time in running a mile. Initially (before they ever raced each other), the first friend runs a mile in 7 minutes, and for each race that they run, his time decreases by 13 seconds. Initially, the second friend runs a mile in 7 minutes and 20 seconds, and for each race that they run, his time decreases by 16 seconds. Which will be the first race in which the second friend beats the first?
6. Profit: The profit P , in thousands of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is
a. Express using functional notation the profit at a production level of 5 items per year, and then calculate that value.
b. Determine the two break-even points for this manufacturer—that is, the two production levels at which the profit is zero.
c. Determine the maximum profit if the manufacturer can produce at most 20 items in a year.
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