Question 6: A real world application of the consumer's [UMP] [30 points] 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 '0 denote the visits to the health club and b the amount of beverages a customer buys there and p1, and pg, be their respective prices. Note that p1, 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 U on the horizontal axis and b on the vertical axis] Label all relevant intercepts and slopes. [10 points] 2. Visits to the health club 'U- and beverage consumption is can be considered as being perfect comple ments. Let the preferences of a customer be given by: U(U, b) = min {1.1, Eb}. What plan would such a customer choose if he is maximizing his utility? Determine the optimal consumption levels U\" and b\". [10 points] 3. A different customer has the following preferences Z (a, b) = min {41.1.5}. In other wordsI 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]