Please help me solve part 4 and part 5 of this problem

The pandemic has shift teaching from the classroom to the Zoom room and with it has made Professors and TAs to adjust their teaching tools. Assume that LoGi is the only company selling microphones to UCLA. LoGi offers two types of microphones \"podcast\" style and \"economy\" style. The following chart shows the willingness to pay and cost for each type of microphone and consumers. Willingness to pay Microphone Costs Professors TAs Podcast 40 200 120 Economy 23 80 30 1. Suppose that LoGi is able to tell apart professors from TAs. Then, LoGi can choose which microphone to offer to each consumer, and what price to charge. Which microphone would LoGi offer to professors and what price would Lo 02' charge? What about the TAs? For items 2-5 below, assume that LoG'z' cannot tell professors apart from T143. 2. Assume that in the mist of the pandemic LoGi decides to sell economy microphones only because it is much easier to produce those. What is the equilibrium price of economy micro phones that would maximize LoGi prots? Hint: Your answer will be a function of the number of professors and TA '3. 3. Now suppose that LoGi decides to sell podcast style micrOphones only. Compute the price that would maximize LoGi prots. 4. LoGi has done some research and learned that there are 15 professors and 85 TAs at UCLA. Based on this, Lo Gt" wants to sell podcast mics to professors and economy mics to TAB. What are the prices of each type of mics that allow LoGi. to do so? 5. Assume prices for each type of mic are those that you computed in the previous question. The Econ department knows that the TAs are buying the economy mics at this price and wants to give them incentives to buy the podcast mics. So, they come up with the following rule, if a TA buys an economy mic she will have to pay for if out of pocket, but if the TA buys a podcast mic, the department will reimburse 3: dollars to the TA. What is the minimum value of a: such that the TAs will be indifferent between buying the economy mic and the podcast mic