Nazar restaurant makes a market analysis to find out that the minimum willingness-to- pay (wtp) for the lunch is $2.5 and maximum wtp is $12.5. Suppose that the wtp is uniformly distributed between these limits, that there are 100 lunch customers considering to go to the Nazar restaurant and that the cost of the lunch is $5. a) (0.5 pts) The restaurant classifies anybody with wtp more than $8.5 as a high-paying customer. The rest are considered low-paying customers. The restaurant will offer a la cart service to high-paying customers and a lunch buffet to low-paying customers. Let d, d denote the demand of high-paying and low-paying customers, obtain the demand functions di(p) and d(p) for 2.5 p 12.5. b) (0.5 pts) If you are told that the demand functions are: d(p) = min {50, 125 - 10p} d(p) = (75-10p)+ at what level of wtp (i.e., at what value of v) is the market split in to high- and low-paying customers? (Note that this number was v=7 on your slides. Try to use minimum value of demand and demand function to obtain the new value of v.) Then, find the optimal prices p* and p* to charge for the markets specified. c) (0.5 pts) What is the total profit when Nazar charges p = 9 and p2 = 6 in the markets specified in part b.