Need mathematical modeling of below problem using linear programming

1. The three children of a farm couple are sent to the market to sell 90 apples. Karen, the oldest, carries 50 apples; Bill, the middle one, carries 30; and John, the youngest, carries only 10. The parents have stipulated five rules: a. The selling price is either $1 for 7 apples or $3 for 1 apple, or a combination of the two prices. b. Each child may exercise one or both options of the selling price. C. Each of the three children must return with exactly the same amount of money. . Each child's income must be in whole dollars (no cents allowed). e. The amount received by each child must be the largest possible under the stipulated conditions. Given that the three kids can sell all they have, formulate the problem as ILP. 2. You are interested in choosing a set of investments {1, ...,7}. Using binary variables, model the following constraints: a. You cannot invest in all of them. . You must choose at least one of them. . Investment 1 cannot be chosen if investment 3 is chosen. d. You must choose either both investments 1 and 5 or neither. e. You must choose either at least one investment 1,2,3, or at least two investments from 2,4,5,6