A small cafe sells drip coffee for $0.95 per cup. On average, it costs the cafe $0.25 to make a cup of coffee(for grounds, hot water, filters). The cafe also has a fixed daily cost of $200 (for rent, wages, utilities).
a) let R, C, and P be the cafe's daily revenue, costs, and profit, respectively, for selling x cups of coffee in a day. Find formulas for R, C, and P as functions of x. [hint: The revenue, R, is the total amount of money that the cafe brings in. The cost, C, includes the fixed daily cost as well as the cost for all x cups of coffee sold. P is the cafe's profit after costs have been accounted for.]
b) Plot P against x. For what x-values is the graph of P below the x-axis? Above the x-axis?