1. Market research suggests that, if the price of a product is $p, then the number of units sold will be q = ap+b, where a and b are constants. (a) If a price of $6 leads to sales of 100 units and a price of $14 leads to sales of 20 units, find the values of a and b. (b) What range of prices is possible? (c) Find the revenue from sales in terms of the price. What price will maximise this revenue? What is this maximum revenue? (4 marks) (3 marks) (7 marks) (d) If revenue is the only consideration, how many units should be sold? (2 marks) (e) Sketch the curve that represents how revenue is changing with price. (4 marks)