SOLUTION: A company that conducts bus tours found that when the price was $9.00 per person,the average number of customers was 1000 per week. When the company reduced the price to $7.00 per

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Question 1114839: A company that conducts bus tours found that when the price was $9.00 per person,the average number of customers was 1000 per week. When the company reduced the price to $7.00 per person, the average number of customers increased to 1500 per week.
(a)Write a linear equation that gives the unit price p, in terms of the average number of customers x per week. (Write your answer in the form p = mx + b.)
b). What unit price should be charged to obtain the greatest weekly revenue?
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39620) About Me  (Show Source):
Answer by stanbon(75887) About Me  (Show Source):
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A company that conducts bus tours found that when the price was $9.00 per person,the average number of customers was 1000 per week. When the company reduced the price to $7.00 per person, the average number of customers increased to 1500 per week.
(a)Write a linear equation that gives the unit price p, in terms of the average number of customers x per week. (Write your answer in the form p = mx + b.)
b). What unit price should be charged to obtain the greatest weekly revenue?
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Revenue = price*# of customers
$2 decrease in price resulted in 500 increase in customers
R(x) = (9-2x)(1000+500x)
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To find "greatest weekly revenue"::
R(x) = 9000 + 4500x-2000x -1000x^2
R'(x) = 2500 - 2000x
Solve:: -2000x = -2500
x = 1.25
Ans: Best price $9-2*1.25 = $6.50
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Cheers,
Stan H.
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