SOLUTION: A tour bus in Boston serves 400 customers a day. The charge is $5 per person. Suppose that for each $0.50 increase in fare, a bus company will lose 8 passengers. Determine how much

Question 1028691: A tour bus in Boston serves 400 customers a day. The charge is $5 per person. Suppose that for each $0.50 increase in fare, a bus company will lose 8 passengers. Determine how much the fare should be in order to maximize the income, and then determine the maximum income.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Income = (5 + 0.50x)(400 - 8x), where x = number of increment times.
==> Income = 4(10 + x)(50 - x), after factoring.
==> The roots are x = -10, 50.
The maximum is attained at the midpoint of -10 and 50, namely x = 20.
==> The fare should be $15 in order to maximize income, and the maximum income is $3,600.
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