The function C(n) = Kn^(-a)is an example of a learning curve. C(n) is the cost of producing the nth unit of a product or service, and K > 0 and a > 0 are constants. The behavior 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 n to estimate the parameters (but that is not a part of this assignment).

Suppose there are two different methods of manufacturing the same product. For method A, KA = $100 and aA = 0.6. For method B, KB = $50 and aB = 0.4. The units of both C(n) functions are dollars.

(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.