As a budding entrepreneur, you have purchased a small bakery. After some market research, you have estimated that your customers' willingness to pay for a donut/coffee combo falls into 9 categories ($2.75, $2.50, $2.25, $2.00, $1.75, $1.50, $1.25, $1.00, $0.75), and you believe that these categories each have roughly the same number of customers. [This means that one group of customers is willing to pay a maximum of $2.75 for a donut+coffee, another equal-sized group is willing to pay a maximum of $2.50, a third equal-sized group will pay a maximum of $2.25, and so on.] Suppose each group has 50 customers so there is maximum potential for 450 customers per week. All of your costs are fixed except labor and materials, which cost $1.10 per donut/coffee combo. Suppose your market research also tells you that the four customer groups with the lowest willingness to pay are all students.

a. Describe the pricing scheme that would maximize your overall weekly profit (assuming you only want to price in $0.25 increments)? Provide all supporting work that justifies this pricing plan.

b. If you follow this optimal scheme, compute your expected weekly profit.

c. Would your optimal pricing scheme change if you realized each group of consumers was comprised of roughly 100 customers rather than 50? Why or why not?