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Question 3 (12 marks) Mark has decided to lay his own turf on a new house block. He is considering getting a local landscape company to supply and deliver the topsoil that he needs for the job. The local company charges $40 delivery within a radius of 15km of the company and $75 per cubic metre of soil. (a) Write down an equation which represents the cost C of delivering z cubic metres of topsoil if Mark lives within the 15km radius of the yard. (2 marks) (b) Draw a graph of the cost equation in part a. Use graph paper and include at least 3 points on the graph. (2 marks) (c) Where does the graph meet the vertical axis and what physical quantity (in the context of this problem) does this value represent? (2 marks) (d) What is the gradient of this equation and what physical quantity (in the context of this problem) does this value represent? (2 marks) (e) Mark has calculated that he needs 4.5 cubic metres of topsoil for his job. How much will he be charged for this if he uses the company to supply and deliver the soil? (2 marks) (f) A second company charges $80 delivery within a 15km radius and $65 per cubic metre of soil. How much soil would Mark have to order so that it is cheaper to purchase the soil from the second company? [Note: this can be solved graphically or algebraically] (2 marks)