This exercise studies the price competition between two major telcos in Australia: Telstra and Optus, and their relationship with NBN (National Broadband Network). NBN is a publicly-owned, open-access data network wholesaler. Telstra and Optus are retail service providers (RSPs) who contract with NBN to access the data network and sell fixed internet access to end users. Currently the most popular home internet plan in Australia is the NBN 50 plan, which provides a theoretical download speed of 50 Mbps. To simplify our analysis, assume NBN 50 is the only plan offered by Telstra and Optus, and they are the only telcos in Australia. Suppose on average NBN charges PN (wholesale price) per customer access to NBN 50 per month to RSPs. Telstra's monthly total cost function is TCT(QT) = (PN + 5)Qr + 12 million, where Qr is the number of subscribers to Telstra's NBN 50 plan. Similarly, Optus's monthly toal cost function is TCo(Qo) = (PN + 5)Qo + 12 million, where Qo is the number of subscribers to Optus's NBN 50 plan. On the other hand, suppose NBN's monthly total cost function is TCN(QN) = 17QN + 85 million, where QN = Qr + Qo is the total number of NBN 50 subscribers. Let Pr denote Telstra's monthly subscription fee and Po Optus's monthly subscription fee. Within a reasonable price range, Qr and Qo are determined by the following equations: Qr(PT, Po) = 4 million 4 million 3 million Pr + Po 25 25 4 million 3 million Qo(PT, Po) = 4 million - Pot PT 25 25 (a) (2 marks) Write down the profit functions for Telstra and Optus