The Amsterdam Music Theater wants to determine the optimal price to charge for its performances. There are currently two kinds of performances: ballet and dance. I Both are produced at constant zero marginal cost. The Amsterdam Music Theater faces four different types of consumers with their willingness to pay as listed in the table below. Each consumer type is equally well represented in the population. Consumer type Fraction of the population 25% 25% 25% 25% A B C D Ballet () Dance () 10 90 50 70 70 50 90 10 a) Consider two alternative pricing strategies: selling the goods separately and pure bundling. For both strategies, determine the optimal prices to be charged and the resulting profits. Which strategy should the Amsterdam Music Theater follow? b) Suppose that the Amsterdam Music Theater considers mixed bundling as well. Is this strategy more profitable than selling the goods separately or in a bundle?