Consider two neighboring businesses, a coffee shop and an ice cream truck. The hourly profit for both depends linearly on the number of customers served during that hour. The coffee shop breaks even (that is, makes zero profit) when 5 customers are served and makes $75 when 20 customers are served, while the ice cream truck breaks even when 2 customers are served and makes $76 when 40 customers are served. A recent study of the neighborhood found that the number of customers who patronize these two businesses changes depending on how sunny it is outside. The study claims that the number of customers who buy coffee decreases at a constant rate of 1 customer per kilolux of measured sunlight e, while the number of customers who buy ice cream increases at a constant rate of 8 customers per kilolux. The study also found that on a typical overcast day, when sunlight creates 1 kilolux of illuminance, the coffee shop has an average of 30 customers per hour, while the ice cream truck has only 2 customers per hour. 1. Find parametric equations for the number of customers served and the hourly profit of the two businesses with respect to the parameter of sunlight measured in kilolux. 2. The sunniest day of the year is projected to measure at 24.3 kilolux. How much money will the ice cream truck make in an hour on that day? How much will the coffee shop make? 3. At what level of sunlight will both businesses make the same hourly profit? How many customers per hour are each of them serving at this level? 4. The ice cream truck brings in $115,000 of profit a year. If the truck is open from 10 am to 8 pm everyday, what is yearly average sunlight level in the neighborhood? Note that I have restricted the upload file format to PDFs. Consider two neighboring businesses, a coffee shop and an ice cream truck. The hourly profit for both depends linearly on the number of customers served during that hour. The coffee shop breaks even (that is, makes zero profit) when 5 customers are served and makes $75 when 20 customers are served, while the ice cream truck breaks even when 2 customers are served and makes $76 when 40 customers are served. A recent study of the neighborhood found that the number of customers who patronize these two businesses changes depending on how sunny it is outside. The study claims that the number of customers who buy coffee decreases at a constant rate of 1 customer per kilolux of measured sunlight e, while the number of customers who buy ice cream increases at a constant rate of 8 customers per kilolux. The study also found that on a typical overcast day, when sunlight creates 1 kilolux of illuminance, the coffee shop has an average of 30 customers per hour, while the ice cream truck has only 2 customers per hour. 1. Find parametric equations for the number of customers served and the hourly profit of the two businesses with respect to the parameter of sunlight measured in kilolux. 2. The sunniest day of the year is projected to measure at 24.3 kilolux. How much money will the ice cream truck make in an hour on that day? How much will the coffee shop make? 3. At what level of sunlight will both businesses make the same hourly profit? How many customers per hour are each of them serving at this level? 4. The ice cream truck brings in $115,000 of profit a year. If the truck is open from 10 am to 8 pm everyday, what is yearly average sunlight level in the neighborhood? Note that I have restricted the upload file format to PDFs
