Please write down your answers pelase show all your wok please

Group A 1 Show that the values of the 79's given in (16} do indeed satisfy the ow balance equations (14) and (14'). 2 My home uses two light bulbs. On average, a light bulb lasts for 22 days (exponentially distributed). When a light bulb burns out, it takes an average of 2 days (exponentially distributed) before I replace the bulb. a Formulate a three-state birthdeath model of this situation. II Determine the fraction of the time that both light bulbs are working. I: Determine the fraction of the time that no light bulbs are working. Group B 3 You are doing an industry analysis of the Bloomington pizza industry. The rate (per year) at which pizra restaurants enter the industry is given byp, wherep = price ofa pizza in dollars. The price of a piaa is assumed to be max(0, 16 .SF}, where F = number of pizza restaurants in Bloomington. During a given year, the probability that a pizza restaurant fails is \"(10 + p}. Create a birthdeath model of this situation. a In the steady state, estimate the average number of pizza restaurants in Bloomington. It What fraction of the time will there be more than 20 pizza restaurants in Bloomington