A company estimates that if x thousand cedis is spent on the marketing of a certain product, Q(x) thousand units of the product will be sold, where Q(x) = 7x 27 + x 2 . (a) Determine the domain of the function defined. [2 Marks] (b) Determine how much of the product will be sold if the company does not spend any money on marketing. [2 Marks] (c) Determine the amount of money the company must spend on marketing to achieve the minimum and maximum quantities. Leave your answers to 2 decimal places. [10 Marks] (d) Determine the maximum and minimum quantities that can be sold. Leave your answer to the nearest whole number. [5 Marks] (e) Determine the marketing expendure ranges on which quantity sold is increasing and decreasing and interpret your solution. [9 Marks] (f) Determine what happens as the company invests an infintely large amount of money on marketing. [6 Marks] (g) Use the information given from (a) to (f) to sketch the curve of Q(x). [6 Marks] 2. (a) The demand and supply functions of a particular good in a competitive market are defined respectively as p = 200q q1 and p = 30+2q. If p and q denote the price and quantity respectively, determine the equilibrium price and quantity. [15 Marks] (b) Let the price and quantity functions of a product be given by p = 2x + k and q = x + 2 respectively, where x is a variable and k is a constant. Find the value(s) of k for which the total revenue function is always positive. [15 Marks]