The price at which a company sells a particular article varies with the quantity it sells. If it charges 13 per article, it sells 3000 articles; if it charges 5 per article it will sell 7000 articles. Let the quantity of articles the company sells be denoted by the variable d (measured in thousands of articles) and let the price be p.

(a) A straight line with d as the horizontal axis and p as the vertical axis passes through the points (3,13) and (7,5). Find the gradient and intercept of this line. If the price is 7.30 what is the demand?

(b) The company decides to increase the supply of articles as the price increases. If the price is 6 it is prepared to supply 3000 articles, at a price of 11 it is prepared to supply 8000 articles. Let the supply of articles by the company be denoted by the variable s (measured in thousands of articles). Take s to be the horizontal axis and p to be the vertical axis. Obtain the equation of the straight line which represents the information above.

(c) Assuming supply=demand, solve the linear equations from (a) and (b) simultaneously. Write your answer for the price and demand in appropriate units