Facing the recent competitive pressure from online sellers, Walmart is considering using the price- matching strategy in order to keep their consumers. Consider an iPad case with marginal cost $20. The demand function is 60-p when the price is p. Suppose that there are two sellers in the market, Walmart and Amazon, and the demand to each seller is determined by the Bertrand criterion (i.e., if two firms have different prices, the seller with the lower price sells its product for a quantity demanded by that price, and the other seller sells nothing. If two sellers set the same price, then they evenly split the quantity demanded at that price.) Suppose that the "price beating" strategy is not available to any seller. Q: Walmart noticed that only a half of its potential customers would also shop at Amazon. The other half will only shop at Walmart and will not ask for a price match. Both groups of customers have the same demand. That is, the demand function for the first group is 30-p/2, and that for the second group is also 30-p/2, where p is the price. Suppose that Amazon's price is $30 and it uses the "price matching" option. Under this situation, Walmart has a unique optimal strategy. Under that strategy, what is Walmart's price and matching strategy? Also, what is Walmart's expected profit?