A coffee shop employs bakers and baristas. For every 15 lattes a barista makes, they need to eat half a croissant. In addition, for every ten lattes a barista makes, they need to drink one latte themselves to keep the energy up. Similarly, every nine croissants made, bakers need to each one croissant themselves. In addition, for every three croissants made, bakers need to drink two lattes. Ultimately, the coffee shop aims to serve lattes and c croissants to the public (not for the consumption of baristas or bakers). a) (6 points) Represent this "economy" as a system of equations. b) (4 points) For the most recent event, = 210 , c = 140 characterises the number of lattes and croissants the coffee shop served to the public. How many total lattes and croissants were made for this event? Justify your answer mathematically. Now suppose that, instead of needing two lattes every three croissants made, bakers need to drink ln(1 + y) lattes if they bake y croissants total. They still need to eat one croissants every nine made, and the needs of baristas remain the same. For an upcoming event, the coffee shop expects to need = 1, 000 lattes for the public. They don't yet know the exact value for c. 2 c) (2 point) Represent this modified economy as a system of equations. d) (1 point) Using economic intuition, explain whether you expect the number of lattes needed will increase or decrease in c. e) (5 points) Does the number of lattes needed increase or decrease in c? Justify your answer mathematically