Competitive Marketing (Adapted from Professor Deshmukh's (Kellogg) lecture notes) Taczan and Mettaga are two prescription drugs that compete in the market for ulcer remedies. Market demand for these drugs is price inelastic, since the patients' purchase decisions are largely influenced by physicians prescribing the drugs. The two drugs, however, compete vigorously in advertising. Marketing managers of the two companies must determine the correct amount to spend on advertising.The total market size is 500 "customers". Advertising media are bought in Gross Rating Points (GRPs), and the cost of buying a GRPs is a 1.5 dollars. If Taczan buys a GRPs and Mettaga buys B GRPs, Taczan's market share is given by 0.9a 0.5 / (0.9a 0.5+ B 0.5), where the advertising effectiveness coefficient c = 0.9 is determined by the creative aspect of advertising. As marketing manager of Taczan, you have to choose the advertising GRPs. You do not know how much Mettaga will spend on advertising, but based on the past experience, you believe that Mettaga's advertising GRPs will vary from a low of 5 to a maximum of 15, with anything in between being equally likely. How many GRPs should you purchase to maximize Taczan's average profit? Assume that unit price of product is $1.