The first coffee shop in LH (a small town of ten thousand residents in the Midwest) is opening in a month. The store is selling freshly brewed coffee in three sizes: small (5 fl. oz.), medium (8 fl. oz.) and large (11 fl. oz.), and the cost of the coffee is 10 cents per fl. oz. The marketing research that the storeowner, Luc, conducted show that there are four thousand people who drink coffee in this town, and they drink at most one cup of coffee each day. His research further shows that 50% of these people are light consumers whose values for the three sizes are $2, $2.2 and $2.3, respectively; 25% of them are regular consumers whose values for the three sizes are $2.1, $2.5 and $2.6, respectively; and the rest are heavy consumers whose values for the three sizes are $2.2, $2.6 and $3, respectively. The consumers' value for drinking no coffee is zero. The consumers are rational: they choose the size that maximizes their surplus, which is defined as "the value - the price". The consumer surplus from not buying any coffee is zero. The goal of the coffee shop is to use the menu pricing strategy to maximize its profit. You are advising the coffee shop on its pricing strategy. Please answer the following questions given the information provided above.

Q1. What is your recommended price (in dollars) for the small size? (0.5 pts)

Q2. What is your recommended price (in dollars) for the median size? (0.5 pts)

Q3. What is your recommended price (in dollars) for the large size? (0.5 pts)

Q4. What is the coffee shop's total profit (in dollars) per day under the optimal menu prices? (0.5 pts)