Marketing Research

The marketing research department of a company that sells air-conditions, established the following price-demand and cost functions:                 𝑝(𝑥) = 1.000−5𝑥                             𝐶(𝑥) = 2.000+500𝑥   where  p(x) is the wholesale price in Euro at which x number of air-conditions (in hundreds)  can be sold and C(x) is the cost in Euro, when x number of  air-conditions are provided. Both functions have a domain of 5 ≤ 𝑥 ≤ 250.  a) Sketch the graph of the revenue function in a rectangular coordinate system.                                                                       (6 marks)  b) Find the value of x that will produce the maximum revenue (correct to the nearest unit).                                                                                                                          (4 marks)   c) Determine the maximum revenue correct to the nearest Euro.                                                                                                                          (3 marks)    d) Calculate the wholesale price per air-condition (to the nearest Euro) that produces  the maximum revenue.