Model the following situations exactly using binary/integer variables and linear constraints: 1. Suppose a consumer derives UA units of utility from product A and UB units from product B. Further suppose UA UB and U > 0 and UB > 0. Model the following consumer choice constraint using binary variables: If both products are shown (presented) to the consumer, the consumer will not choose the product with lower utility (notice that the consumer may choose none of the products.) 2. A group of friends are browsing through the local video store, trying to decide which movies to rent. The friends, all ISB students, would like to plan their movie-watching schedule using integer programming. Write exactly one binary variable constraint to model the following statement: "If we rent both Bahubali II (B) and Dangal (D), then we can rent at most one of Drishyam (R), The Lunch Box (L), and Bhaag Milkha Bhaag (M)." 3. Suppose a broker must choose to invest in four investments 1, 2, 3, and 4. Let x1, x2, x3, and 4 denote the binary variables if she chooses the particular investment or not. Suppose she has the following constraints: If she invests in 3 or 4 or both then she must invest in exactly one of 1 or 2. Otherwise, if she invests in neither (of 3 or 4) then there are no constraints on investing in 1 or 2.