A health club offers two different plans for its visitors. Under plan A, no membership is required and each visit costs $10. Under plan B, an annual fee of $200 is paid to become a member and each visit costs only $4. It also sells beverages at a unit price of $10. 1. Let 1) denote the visits to the health club and b the amount of beverages a customer buys there and pv and p5 be their respective prices. Note that pv differs for each plan. Assuming that the potential customers have an annual income of $1000, draw the budget constraints under the two plans on the same graph. [Place 1) on the horizontal axis and b on the vertical axis] Label all relevant intercepts and s10pes. [10 points] 2. Visits to the health club -v- and beverage consumption -b can be considered as being perfect comple- ments. Let the preferences of a customer be given by: U (c, b) = min {1), 3b}. What plan would such a customer choose if he is maximizing his utility? Determine the Optimal consumption levels 12* and b*. [10 points] 3. A different customer has the following preferences Z (1), b) = min {41}, b}. In other words, this customer tends to drink more in each visit than the customer in part (b). What plan would this customer choose? Again, determine the optimal consumption levels v** and b**. [10 points]