Prove that the above ilp is an ilp formulation of set cover. in other words, give a one-to-one mapping between feasible assignments to the variables x s and p subfamilies f 0 ⊆ f such that c(f 0 ) = u, and such that |f 0 | = s∈f x s .

Item 1 which question could the expression 1000n answer? let n = the number of gallons of gas used. how many miles per gallon did the car get driving 1000 miles? let n = the number of grams of food needed for each dog. how many grams of food are needed to feed 1000 dogs? let n = the number of people at the show. how many empty seats were there at the show if there are 1000 seats at the theater? let n = the number of seats at the theater. how many empty seats will there by if 1000 people come to the show?