A company producing bicycles hires a mathematician to study how the number of sales depend on the price. Using a machine learning algorithm, the mathematician
finds that this can be approximated by
p
N(p) = 10 -
where N is the number of sales in a week and p is the price at which one
bike is sold.
a) According to this model, what is the weekly revenue if the price is fixed
to 100 pounds?
[2 mark]
b) Can this model for N(p) be valid for any value of the price? Explain why, using words and equations.
[The answer to this part of the question must be typed in own words.]
[2 marks]
c) What price p should the company choose if they want to maximise the number of weekly sales?
Sample Solution