The function 001) = K 710\" is an example of a learning curve. 0(a) is the cost of producing the n'th unit of a product or service, and K > 0 and a. > 0 are constants. The behaviour of the learning curve changes with the value of the constants K and a, which can be called parameters of the model. Different values describe different production processes. If you believe a process should correspond to this class of model, you could use data at different 11 to estimate the parameters (but that is not a part of this assignment). 2. (**7(jf) Calculate the following limits, and then explain what each means in terms of the physical phenomenon being described. (a) (1 mark) lim C(n). TL>00 (b) (1 mark) lim Own). 71,)00 3. (2 marks) (*jr) According to this model, are efficient industries associated with a relatively small parameter a, or with a relatively large parameter a? Explain your answer carefully. 4. (****) Suppose there are two different methods of manufacturing the same product. For method A, KA = $100 and (1,4 = 0.6. For method B, K3 = $50 and a3 = 0.4. The units of both C(n) functions are dollars. Note: You can use a spreadsheet program like Excel for this question. (a) (7 marks) Find both the cheapest and most expensive method for manufacturing 100 units. You may mix methods. That is, produce some with method A and others with method B. Note that the production with method A will not help the learning for method B and vice versa. (b) (2 marks) Suppose instead of 100 units, you are asked to describe the cheapest method for manu- facturing N units. Find the N at which there is a change in the production strategy used for the cheapest solution. (c) (2 marks) Explain your result from (c) above. 5. (2 marks) (**'"ff) The model can also be used to to describe the time taken C(n) for a task that you are doing for the n'th time. Consider the task of cooking a specic meal, cleaning the bathroom, or preparing a Math 100 lecture. The behaviour described in #2 (a) should not quite t your expectations in these cases. What (simple) modication could you make to the model to make it more realistic